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ELEMENTARY PHYSICS FOR ENGINEERS

CAMBRIDGE UNIVERSITY PRESS

C. F. CLAY, Manager

iLonHon: FETTER LANE, E.G.

enmburgt): loo PRINCES STREET

fitia lorfe: G. P. PUTNAM'S SONS Bombag. Calcutta anH fSaUraB: MACMILLAN AND CO., Ltd. Coronto: J. M. DENT AND SONS Ltd. ffokBo: THE MARUZEN-KABUSHIKI-KAISHA

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ELEMENTARY PHYSICS FOR ENGINEERS

AN ELEMENTARY TEXT BOOK FOR FIRST YEAR STUDENTS TAKING AN ENGINEERING COURSE IN A TECHNICAL INSTITUTION

BY

J. PALEY YORKE

Head of the Physics and Electrical Engineering Department

at the London County Council School of Engineering

Poplar, London

Cambridge :

at the University Press

1916

PREFACE

THE importance of Physics to the engineer is in- estimable but the student of engineering does not often recognise the fact.

This little volume is intended to appeal to him firstly because it is written specially for him and secondly because the author has attempted to present some essential facts of elementary physics as briefly and straightforwardly as possible without any pedantry or insistence upon details of no practical importance. He has also avoided all reference to historical deter- minations of physical constants and has described in all cases the simplest and most direct methods, merely indicating the directions in which refinements might be made. At the same time he has endeavoured to make no sacrifice of fundamental principle and no attempt has been made to advance with insufficient fines of communication.

The author frankly admits that he has tried to be interesting and readable, and in case this should be regarded as a deplorable lapse from the more generally accepted standards he pleads the privilege of one who has had considerable experience with students of engi- neering in Technical Institutions.

He hopes by this little volume to induce a greater number of engineering students to recognise that Physics is as essential to engineering as is Fuel to a Steam Engine.

J. P. Y.

London, 1916.

CONTENTS

CHAPTER I

MATTER AND ITS GENERAL PROPERTIES

Definition of matter. Weight. Force. Mass. Inertia. Theory of structure of matter. Indestructibility of matter. Classifi- calion of matter. Solids, liquids and gases. Density. Modes of determination. Elasticity. Strain and stress. Hooke's Law. Modulus of Elasticity . . . pages 1-14

CHAPTER II PROPERTIES OF LIQUIDS

Pressure produced by liquids. Pressure at different depths. Upward pressure. Pressure at a point. Pressure on sides of a vessel. Buoyancy. Floating bodies. Archimedes' principle. Specific gravity or Relative density and modes of determination. Hydrometer. Pumps. Capillarity. Surface Tension. Diffusion. Viscosity 15-36

CHAPTER III

PROPERTIES OF GASES

Weight. Pressure exerted equally in all directions. Atmospheric pressure. The Barometer. The relationship between volume and pressure 37-47

CHAPTER IV

FORCE, WORK AND ENERGY

Units of Length, Mass, Time and Volume on British and metric systems. Force. Units of Force. Work and its measurement. Examples on both systems. Energy. Potential and kinetic energy. Various forms of energy. Principle of conservation of energy. Power 48-56

Contents vii

CHAPTER V HEAT AND TEMPERATURE

Production of heat. General effects. Distinction between Heat and Temperature. Measurement of Temperature. Fixed points. Construction and calibration of Mercury Ther- mometers. Scales of Temperature. Other Thermometers. Pyrometer. Self-registering Thermometers. Clinical Ther- mometer 57-71

CHAPTER VI EXPANSION OF SOLIDS

Laws of expansion. Coefficient of Unear expansion and mode of determination. Some advantages and disadvantages of the expansion of solids. Superficial expansion. Voluminal ex- pansion . "^ . . 72-80

CHAPTER VII EXPANSION OF LIQUIDS

Real and apparent expansion. Modes of determination of co- efficients. Peculiar behaviour of water. Temperature af maximum density 81-85

CHAPTER VIII EXPANSION OF GASES

Charles' law and mode of experimental verification. Variation of pressure with temperature. Absolute zero and absolute scale of temperature 86—94

CHAPTER IX MEASUREMENT OF HEAT

Units of heat on different systems and their relationship. Specific heat. Water equivalent. Measurement of specific heat. Calorific value of fuels. Mode of determination. Two values for the specific heat of a gas .... 95-106

viii Contents

CHAPTER X FUSION AND SOLIDIFICATION Change of physical state by application or withdrawal of heat. Melting and freezing point*'. Heat required to melt a solid. Latent heat of fusion. Melting points by cooling. Change of volume with change of state. Solution. Freezing mixtures. Effect of pressure on the melting point . 107-114

CHAPTER XI VAPORISATION Vaporisation. Condensation. Evaporation. Ebullition. Boiling point. Effect of pressure on boiling point. Temperature of steam at different pressures. Heat necessary for vaporisation. Vapour pressure. Boyle's law and vapour pressure. Tem- perature and vapour pressure. Latent Heat of vaporisation. Sensible Heat and Total Heat. Variation 6f Latent Heat of steam with temperature. Pressure Volume and Temperature of saturated steam. Hygrometry. The dew-point . 115-132

CHAPTER XII

TRANSMISSION OF HEAT

Conduction. Thermal conducti\'ity. Examples and appUcations of conductivity. The safety lamp. Conduction in Uquids. Convection in liquids. Hot water circulation. Convection in gases. Ventilation and heating by convection. Radiation. Reflexion and absorption of heat-energy. Transmission and absorption of heat-energy. Radiation from different surfaces at equal temperatures. Flame radiation. Dew formation.

133-148

CHAPTER Xm THERM9-DYNAMICS Mechanical equivalent of heat and mode of determination. Funda- mental principle of the heat engine. Effect of compression and expansion on saturated steam. Isothermal and adiabatic ex- pansion. The indicator diagram .... 149-162

Index 163-165

CHAPTER I

MATTER AND ITS GENERAL PROPERTIES

We all know that there are many different states or conditions of matter. Ice, water and steam are three different conditions of exactly the same kind of matter ; they differ only in having distinctive physical pro- perties, being constitutionally or chemically identical. Though they have certain distinctive characteristics — such for example as the definite shape of a piece of ice and the entire lack of shape of water or steam : the definite volume of a given weight of water and the indefiniteness of the volume of a given weight of steam which can be compressed or expanded with ease — they have nevertheless certain properties in common with all other forms of matter.

Indeed it is common to define matter as that which occupies space or that which has weight. Each of these definitions names a property common to all matter. It seems rather unnecessary to try to define matter : we feel that everyone must know what matter is : and the definitions are likely to introduce ideas more diffi- cult to appreciate than the thing which is being defined. But we can see nevertheless that it may be useful and even necessary to have some definite dividing line between matter and the various sensations which can proceed from it. The colour of a rose is merely a sensation : its perfume is the same : but the rose

p. Y. 1

2 Matter and its General ProperticH [CH.

itself is matter. Our distinction is that the rose lias weight and occupies space. Colour has no weight, nor does it occupy space.

Again when a piece of coal is burning it is giving out Heat. Is that heat matter ? Well, if we ap})ly the test of weight to it we find that it is not. A hot object weighs neither more nor less than the same object cold. If we weigh the coal before it is ignited and then while it is burning if we collect all the products of the burning — that is to say all the gas and smoke and ash — we should find that there was no change in weight. This is a well-known experiment — though usually done with a piece of candle instead of coal — and it is being mentioned now to shew that though this burning matter is giving out heat, and also light, yet these things are weightless and are therefore outside our definition of matter. For if they had weight then the mere residue of the ash and the fumes would not have had the same weight as the original matter. We will return presently to the further question of how we shall classify Heat.

The experiment quoted above is one of many which have led us to the firm belief that matter cannot be destroyed. We can change its form both physically and chemically but we cannot annihilate it. This is one of the fundamental law* of physical chemistry and one of the greatest importance and usefulness.

Weight. All forms of matter possess weight. It is to be supposed that all readers know what is meant by the statement. In books of this kind much space and many words are used to convey to the readers' minds ideas with which they must already be sufficiently famiHar. W^e explain that Force is that which produces

i] flatter and its General Properties 3

or tends to produce motion : that it is also that which is necessary to destroy motion : that it is also necessary if the direction of motion of a body is to be changed. We then proceed to define motion as the change of position of a body with respect to some other body; and we may even devote some space to the explanation of what position is. It is extremely probable that everyone knows these things, though it is very likely that only a few could frame their knowledge in words.

In the same way weight is the attraction between every portion of matter and the earth. This attraction tends to draw everything vertically downwards towards the earth. It is called the force of gravitation ; but nobody has the least idea why the earth attracts things or what this mysterious force is. We are so used to it, it is so continiially present that we take it quite as a matter of course, and never pause to consider that it is mysterious and inexplicable. The attraction of a needle to a magnet fills us with wonder or awe but the attraction of a stone to the earth seems to be inevitable and ordinary.

Weight then is a/orce ; it is a particular force which acts only in one direction upon matter, and that direction is vertically downwards. Of course the force is also tending to pull the earth vertically upwards, but the reader will have no difficulty in appreciating the fact that no movement of the earth as a whole would be detected by us. We can think of every portion of matter being attached to the centre of the earth by imaginary stretched elastic threads. These threads will be in tension and will tend to shorten by pulling the object and the earth towards each other. The pull will be equal in both directions — but when we think

1—2

4 Matter and its (Sineral Properties [CH.

of the enormous mass of the earth compared with the mass of the object we may be considering we can readily see that the object will go downwards much more than the earth will come up. At the same time we can see the tendency and in seeing that we are also seeing something of a very important mechanical law about the reaction which accompanies every action.

We say then that matter is that which possesses weight. Air and all other gases can be weighed by taking a flask, exhausting the air from it by means of a vacuum pump, weighing it carefully, and then allowing either air or any other gas to enter it when it can be weighed again. The increase in weight will represent the weight of that flask of the gas at the particular pressure under which the flask was filled. If a higher pressure were used then, as more gas would be forced into the flask, the increase in the weight would be correspondingly greater.

Mass. This leads us naturally to the meaning of the word mass. By the mass of a body we mean the quantity of matter in it. This is often confused with bulk or volume and of course the greater the volume of any one particular kind of matter the greater must be the quantity of that matter. But on the other hand is there the same quantity of stuff in a cubic foot of cork as there is in a cubic foot of lead ? Is there the same quantity of steam in a given boiler, with the water level at a certain point, whatever the steam pressure may be? The answers will suggest that we cannot compare the masses of different kinds of matter by comparing their volumes.

It is usual to compare masses of matter by weighing them. A quantity of cork weighing 1 pound contains

i] Matter and its General Properties 5

the same quantity of matter as a piece of lead weighing 1 pound. At the same time we must be careful to remember that weight is simply the force of attraction between the matter and the earth and that mass is the quantity of stuff in it. When we ask for a pound of sugar we want a mass of it which is attracted to the earth with a force of 1 lb. weight.

It may help us to see this distinction if we remember — as most of us probably do — that a given object has slightly different weights or forces of attraction at different parts of the earth, owing to the shape of the earth and to the fact that at some places we are nearer to its centre than at others. Well, although an object may have different weights, yet we know that its mass must remain the same. This helps us to see the dis- tinction between the two — though it may suggest certain difficulties in buying by weight from different parts of the earth. As a matter of fact the difference is very slight — about two parts in a thousand at the outside — and if the substances be weighed with balances and "weights" we can see that the "weights" will be equally affected and that we should get equal masses from different places. But if spring balances be used then a pound weight of sugar sent from a place far north would be a smaller mass than a pound sent from a place near the equator.

The reader will learn in the mechanics portion of his course of study how masses may be compared in other ways in which the weights are eliminated.

Inertia. There is another property, called Inertia, which is common to all forms of matter. When we say that matter has inertia we mean {a) that it cannot start to move without the application of some force.

() Matter and its General Properties [cH.

(6) that, if moving, it cannot stop without the appli- cation of force, (c) that if moving in any particular direction it will continue to move in that direction unless some force or forces be applied to it to make it change its direction. That is to nay force is necessary to overcome inertia.

Inertia is not a cause and it is not a reason. It is the name given to the fact that every object tends to remain in whatever condition of motion or rest it may be at any given moment. That tendency means that it is very difficult to start'anything suddenly/ or to stop it suddenly or to change its direction of motion suddenly. Experimental verification of these truths may be ob- tained by anyone during a short journey in a tramcar. If one is standing in a stationary car, scorning the friendly aid of "the strap," and the car starts abruptly one learns that matter (oneself in this case) tends to remain in its previous condition of rest, and that straps are really useful adjuncts of the car.

If the motorman suddenly applies his brakes and reduces the speed of the car the passengers shew a unanimous tendency to continue their previous speed by side-slipping along their seats in the direction of the car's motion. If one is walking towards the con- ductor's end during this slowing down process one finds considerable difficulty in getting there, just as though one was climbing a very steep hill against a stiff breeze. If one is walking towards the motorman's end and he slows down one finds it difficult not to run . In rounding a sharp curve — that is'to say changing the direction of motion — there is always the tendency to be thrown towards the outside of the curve, shewing the tendency of moving matter to continue in its original direction.

i] Matter and its General Properties 7

There are countless examples of tljis property of matter. A hammer head reaches a nail, but it does not stop suddenly : the distance the nail is driven in depends on the kind of nail and the substance and the weight and the speed of the hammer. Chiselling, forging, pile-driving, wood-chopping, stone-breaking and cream- separating are amongst the many processes which depend upon the fact that matter possesses inertia. The "banking" of railway tracks at all curves so that the outer rail is higher than the inner is necessary to assist the train to change its direction of motion. When a motor car or a bicycle side-slips it is due to the tendency to continue in its original direction and if it is taken round the corner too sharply the result will be side-slipping or overturning to the outside of the curve. Most people fondly believe that if a cart is taken too suddenly round a bend it will fall inwards. Let the reader ask any half-dozen of his friends.

Then we know how difficult it is to start moving on a very slippery floor, or on ice, and how equally difficult it is to stop again. It is not suggested here that one's inertia is any greater than it would be on a rough floor : the point is that one cannot get a "grip" and thus cannot exert such a large force either to start or to stop. The skidding of a locomotive when starting with a train of great mass is another example of this point.

Theory of Structure of Matter. In order to explain and connect the many facts of nature it is necessary that we should have some idea of the structure of matter. The generally accepted theory is that known as the kinetic theory, a theory which assumes that all substances are composed of an enormous number of

H M<itter and Its General Properties [ch.

very small particles or grains called molecules. Further it assumes that these molecules are not generally in contact with their neighbours but are in a state of continued agitation and vibration ; that collisions between them are of frequent occurrence ; that even when any two or more are in contact with one another there are distinct interspaces between them called inter-molecular spaces.

According to this theory a portion of matter is not continuous substance but a conglomeration of small particles which attract one another with a force called cohesion.

The motion of the molecules in solid matter is very restricted : it is probably rather in the nature of vibration or oscillation than migration. In liquids the molecules are not supposed to be so close together and thus may thread their way through the mass like a person in a crowd. In the case of gases the spaces between the molecules are assumed to be still greater so that the molecules can move about with considerable freedom.

It is also believed that the hotter a body is the greater does the movement and vibration of each molecule become. That is to say, the energy of move- ment of each molecule is increased as the temperature is increased. Indeed from this theory it is argued that if the temperature could be lowered until there was no molecular agitation there could be no heat in the body and such a temperature would be the absolute zero of temperature.

Classification of matter. Apart from the properties which are common to all kinds of matter there are other properties which are peculiar to one form or

i] Matter and its General Properties 9

another. Such properties enable us to classify matter into different groups. In physics such classification is based solely upon physical properties and our groups are only three in number namely, solids, liquids and gases. Sometimes indeed it is said that there are only two groups, solids and fluids, the word fluid including liquid and gas.

Solids are distinguished from fluids — that is from liquids and gases — in that each portion of a solid has a definite shape of its own. This property is termed rigidity. Liquids and gases have no rigidity : a portion of a hquid has no definite shape though it has a definite volume : a given weight of a gas has no definite shape, and its volume depends upon the pressure acting upon it. This latter fact helps us to distinguish between a liquid and a gas. A liquid is practically incom- pressible but a gas is readily compressed.

A fluid cannot resist a stress unless it is supported on all sides.

Density. Though all forms of matter have weight yet if we take the same bulk or volume of different forms such as cork, #ater, lead and marble we shall find that they have different weights.

The mass of a unit volume of a substance is called the density of that substance.

If we know the density of a substance we can calculate either the mass of any known volume or the volume of any known mass.

On the British system of units density would be expressed in pounds per cubic foot. On the metric system it is expressed in grammes per cubic centimetre.

Thus the density of pure water (at 4° C.) is 62-4 approximately on the British system and 1 on the

10 Matter and its General Properties [en.

metric system. I^ead is 705-12 on the British and 11-3 on the metric. Of course in both systems the lead is 11-3 times as heavy as the same bulk of water. (See Chapter II.)

For the determination of the density of a substance it is only necessary to be able to weigh a portion of the substance and then to find its volume. If the substance has a regular form its volume can be calculated. If it be irregular it can be immersed in water and the volume of displaced water can then be measured. There are many simple methods of obtaining and measuring the displaced water. There is the obvious method of placing a label to mark the level of water in a vessel and then placing the substance in the vessel. The water above the label mark is now sucked out by means of a pipette until the level is restored. The volume of the water removed must of course be that of the sub- stance and it can be measured in a graduated vessel.

tA^

n

=^w

— , ,

'"

-1-

==.=^—

.-_— _

~-~

_-_— .

— -

(a)

a

W

^

Fig. 1 Fig. 1 illustrates special forms of vessels designed to facilitate the collection and measurement of the dis- placed water. In (a) the vessel i» filled up with water and allowed to adjust its level through the side spout.

I]

Matter and its General Properties

11

A dry measuring vessel is then placed under the spout and the substance whose volume is required is carefully lowered into the water. The other form (6) is called a volumenometer and it utilises a small siphon with the ends drawn out to fine points. This prevents the siphon from emptying itself. Its use is obvious.

More refined methods depend upon weighing instead of measuring the displaced water (as with the specific gravity bottle) and upon the principle of Archimedes. The reader will be able to appreciate these after reading Chapter II.

Densities of some common substances.

Substance

Density in lbs. per cubic foot (approx.)

Density in grammes per cubic centimetre *

Platinum

1344

21-522

Gold

1200

19-245

Lead

712

11-^

Silver

655

10-5

Copper

549-556

8-8 -8-9

Iron (wrought)

466-487

7-47-7-8

Iron (cast)

378-468

6-9 -7-5

Steel

435-493

7-73-7-9

Brass

505-527

8-1 -8-45

Oak

43-2-61-9

0-69 to 0-99

Water

62-4

1

* Since the mass of 1 cubic centimetre of water is 1 gramme it follows that the density of a substance in grammes per cubic centi- metre is numerically equal to its relative density or specific gravity with respect to water (see page 25).

Properties of Solids. Different solids differ from one another not only in chemical composition but also in physical characteristics. Such properties of solids as porosity, hai-dness, malleability, ductility,

12 Matter and its (itcueral Properties [CH.

plasticity and elasticity are shewn in various degrees in different substances. The nature of the properties denoted by the words above is generally understood — with the exception, perhaps, of that property called elasticity.

Elasticity. If the reader were asked to state what was the most highly elastic substance we know of he would probably give india-rubber without much hesitation. Now elasticity is measured by the mag- nitude of the force which is necessary to produce a given change in the shape of a substance : and for such comparison it is necessary that all the substances used be of the same original dimensions. If we were going to compare elasticity so far as stretching is concerned then we would use wires of equal length and equal diameter and we would find out what weights we should have to load on the bottom end in order to stretch them by the same amount. That substance which required the largest weight would have the gTesii^st elasticity.

Of course it would be necessary to see that when the weiglits were removed again the wires returned to their original lengths. If they did not — that is if they were permanently stretched — then we must have loaded them beyond their limits of elasticity. Some substances can be temporarily stretched to a great extent and such are said to have wide limits of elasticity. Thus india- rubber has not a very high degree of elasticity — that is to say it is easily stretched — but it has very wide limits of elasticity. Steel has a high degree of elasticity but very narrow limits.

The same statements apply to compression, to bending and to twisting.

Stress and Strain. When the form or shape of a

i] Matter and its General Properties 13

body has been altered by the apphcation of a force the alteration is called a strain. If a piece of india-rubber is stretched (from 6 inches to 7 inches) the change is called a strain. The same term would be used if it was compressed to 5 inches, or twisted round through any number of degrees, or bent to form an arc. The force producing the strain is called a stress. In strict usage the word strain is used to denote the change produced per unit of length. In a case of stretching for example the extension per unit length of the sub- stance is the strain. If a wire be 60 inches long and it is extended by 1-5 inches then the strain is

Similarly stress is used to denote the force per unit area of cross section. Thus if the wire quoted above has a diameter of 0-05 inch and the stretching force was 10 lbs. weight the stress would be 10 -^ area of cross section of the wire

= 5095 lbs. per sq. inch.

3-14 X (-025)2

Hooke's Law. From a series of experiments Hooke deduced the law that within the limits of elasticity the extension of a substance is directly proportional to the stretching force.

It may also be expressed that strain is directly

proportional to stress. The ratio of - — ^ for any

stram

substance is called Young's modulus for that substance.

This is an important quantity in that section of

engineering work dealing with the strength of materials.

Hooke's law also applies to twisting. If a wire be

^

11 Mutter and its (Icneral Projtcrticn [CH. i

rigidly fixed at one end and a twisting force applied to the other the angle of twist or torsion will be directly proportional to the twisting force. It also applies to bending. If a beam be laid horis^ontally with each end resting on a support and it be loaded with weights at the centre it will bend. The extent to which the centre of the beam is depressed vertically below its original position is called the deflexion of the beam. The deflexion is directly proportional to the bending force. It will be obvious that in all these cases — stretching, compressing, twisting or bending — the amount of change produced will depend not only upon the force applied but also upon the original length of the substance, upon its cross sectional area and upon the particular material used.

EXAMPLES (See table above for densities)

1. What is the weight of a cyUnder of copper (a) in lbs., (b) in grammes, if it is 6" high and 2" diameter and an inch is approxi- mately 2"54 cms. ?

2. What would be the volume of a piece of gold which would have the same weight as 1 cubic foot of silver?

3. If sheet lead costs £27 per ton, what will be the cost of a roll 32 feet long, 3 feet wide and J" thick ?

4. What is the density of the sphere which weighs 4 lbs. and has a diameter of 3 inches ?

5. In what proportions should two liquids A and B be mixed so that the mixture shall have a density of 1-2, the density of A being 0-8, that of 5 1-6.

6. A wire of diameter 0-035 inch and 6 feet long is found to become longer by 0-25 inch when an extra weight of 14 lbs. is hung on to it. What is the stress and the strain and Young's modulus of elasticity ?

CHAPTER II

PROPERTIES OF LIQUIDS

As we have seen liquids have no rigidity and there- fore have no definite shape. A given mass of Hquid will always assume the shape of the portion of a vessel which it occupies. Moreover a liquid is practically incompressible and in this respect it differs from those fluids which we call gases.

If we place some water in a vessel we know that the weight of the water must be acting on the base of that vessel. But we also know that the water does not

/

Fig. 2

merely exert a downward pressure. If holes are pierced in the vessel at positions A and B — as shewn in Fig. 2 — we find that the water streams out through

16 Properties of Llqukh [CH.

thoni aiul that it comes out from B with a greater velocity than from A. This indicates firstly that the wat«r must be exerting horizontal pressure on the sides of the vessel : and secondly that the pressure at B is greater than that at A .

Pressure at different depths. It does not require any deep reasoning to realise that as we pour more water into a given vessel the downward pressure upon its base must increase and that the greater the depth of liquid the greater will be this downward pressure.

If we did not conduct any investigations we might be led to conclude that if we place a piece of cork sufficiently- far below the surface of water it would sink — forced downwards by the enormous pressure which would be exerted at a great depth. But our experiences — that is to say our investigations, whether they were deliberate or casual — tell us that this is not true. Our experiences tell us that when we put our hands under water we are not conscious of an extra weight upon them : that when w^e put them at greater depths we are not conscious of any greater weight than when they were near the surface : that, in fact, we are conscious that our hands seem to be altogether lighter ^when held under the water and that different depths do not appear to make any difference at all upon the sensation of lightness. Our experiences teach us that when we dive into water, instead of being weighed down by the weight of water above us we are in fact buoyed up and we ultimately come — at any rate those of us who are reading must" always have come — to the surface.

Well then, our experiences tell us that somehow or other there appears to be an upward pressure in a

11]

Properties of Liquids

17

liquid. One simple experiment to illustrate this is to take a piece of glass tube open at both ends ; close one end by placing a finger over it ; place the tube vertically in a tall jar of water with the open end downwards. A little water will be forced up the tube — compressing the air inside. As it is lowered further more water will be forced up the tube and the air inside will be more compressed. There must be some upward pressure to do this. Then remove the finger from the top : water will rush up the tube and may even be forced out through the top in the first rush. Ultimately it will settle down so that the water level inside the tube is the same as that outside — suggesting therefore that this upward pressure at the bottom of the tube is exactly equal to the downward pressure there.

ILL

(a) (h)

Fig. 3

A more convincing experiment is illustrated by Fig. 3. A fairly wide glass tube open at both ends has one end carefully ground flat and a circular disc

1 }{ Properties of Liquids [CH.

of aluminium is placed against this end. It is held tightly on by means of a piece of string passing up through the middle of the tube. It is then immersed in a tall jar of water — the disc-covered end downwards — and it is found that the string is no longer necessary to hold on the disc. The upward pressure on the bottom of the disc is sufficient to hold it on.

If now some water be poured carefully into the tube it will be found that the disc will not fall off until the level of the water inside the tube is very nearly equal to that in the jar. If the disc were made of a substance of the same density as water it would hold on until the level was quite up to that in the jar. This experi- ment shews very clearly that the upward pressure on the bottom of the disc was equal to the downward pressure which would have been exerted on it if it had been immersed at the same depth — for when the tube was filled with water to the same depth as in the jar we found that the downward pressure of this depth just counter-balanced the upward pressure — making due allowances for the weight of the disc.

In addition to this it can be shewn by a similar experiment that the liquid exerts a horizontal pres- sure and that the horizontal pressure is also equal to the downward and the upward pressures : that in fact at a given point in a liquid there is a pressure in every direction and that it is equal in every direction.

Pressure at a point. It is necessary that we should have some clear idea of what is meant by the pressure at a given point in a Hjg[uid. If we consider the base of a vessel, for example, it is clear that the weight of water on the base depends not only upon the height of water above it but also on the area of the base. And

ii] Prope7'ties of Liquids 19

since different vessels may have different base areas it will be necessary for us in speaking of pressure at any point to speak of the pressure per unit area at that point. We may speak of the pressure per square foot or per square inch or per square centimetre, and the total pressure on any base will be the pressure per square unit multiplied by the number of square units contained in the base.

Let us suppose that we have a rectangular vessel having a base area of 1 square foot and that it is filled with water to a height of 1 foot. There is therefore 1 cubic foot of water weighing 1000 ozs. resting on a square foot of base. Since there are 144 square inches in the square foot the pressure per square inch must be ^fff- = 6' 94 ozs. (approx.). We can say therefore that the pressure at any point on that base area is 6-94 ozs. per square inch. And further whatever the shape or size of the base may be if the water above it is 1 foot high the pressure per square inch on the base will be 6-94 ozs.

Pressure at a point depends only on vertical depth and density. This last statement needs substantiation. An experiment may be performed with a special U-tube — shewn in Fig. 4 {a) — which is provided with a screw collar at sc on which different shaped and sized limbs may be screwed. Different limbs are shewn in (6), (c) and (d). It is found that if water be poured into the U-tube it will always rise to the same level on each side whatever the shape or size of the limbs may be. Since it follows that when the liquid comes to rest the pressure exerted by the water in the two limbs must be equal, therefore the pressure produced at a given point is not dependent on the size or shape or quantity of water

2—2

i}(»

Properties of Li</ui{ls

[ni.

in I Ik- vrs.st'l hul only upon the verfical depth (see {(J)) of the point beh)\v the surface and u])on tlie density of the liquid. Aiid it follows that if we have a number of vessels having equal bases but having different shapes and volumes the pressure on the bases will be equal if they contain only the same vertical depth of the same liquid. The explanation of this fact may not be very obvious to the reader, but if he has any knowledge of elementary mechanics he will know that there will be "reaction^' at every point of the walls of the vessel. If these walls be quite vertical as in (a), then the re- actions will be horizontal and will balance one another,

but in the case of inclined walls the reactions, which will be at right angles to the wall, will therefore add to the mere water weight on the base in (c) whilst they will counterbalance the extra water weight in the case (6).

Therefore in speaking of the pressure at a point in a liquid we have only to think of the vertical depth of that point and the density of the liquid. At a point 1 foot below the supface of water the pressure is 6*94 ozs. per sq. inch in every direction: at a point L feet below it will be Z- x 6-94 ozs. per sq. inch. If the liquid be D times as heavy as water bulk for bulk

II J Properties of Liquids 21

then the pressure at any point L feet below the surface will be Z) X iy X 6-94 ozs. per square inch.

On the metric system it is even simpler because 1 cubic centimetre of water weighs 1 gramme. There- fore the pressure per square centimetre at any point below the surface will be D x L grammes, where L = depth of the point in centimetres and D = the number of times that the liquid is heavier than water. On the metric system this D will be the density in grammes per cubic centimetre.

Pressure on the sides of a vessel. Since at any given point the pressure is equal in all directions it follows that the pressure on the sides or walls of a vessel at any point is determined in exactly the same way as it would be for a point on a horizontal surface at the same depth. But of course it will be seen that the pressure on the walls increases gradually with the depth and that the total pressure on the side can only be found by deter- mining the pressure on each unit area and adding them all together.

If the vessel has rectangular sides then we can get the total pressure very simply by finding the pressure at a point half-way down from the surface of the liquid to the bottom and multiplying this by the total number of square inches (or cms., according to units used) which are under the water.

For example, in the case of the tank shewn in Fig. 5, which is a cubical tank of 6 foot side filled to a depth of 5 feet with water, the average pressure on one side will be the pressure at a depth of 2-5 feet below the surface. This is 2-5 x 6-94 ozs. per square inch which is 17-35 ozs. per square inch. There are 5 X 6 = 30 square feet below the water and since

22

Properties of Liquids

[CH.

there are 144 square inches to the square foot it follows that the total pressure on the side will be

144 X 30 X 17-35 ozs. = 74952 ozs. = 40845 lbs.

The total pressure on the base will be

(5 X 6-94) X 6 X 6 X 144= 179,885 ozs.

Fig. 6

In the same way the total pressure on a lock gate would be calculated though in that case there would be some water on both sides of the gate at the lower portion. Further, though we get the total pressure in this way it is not of much use in designing a lock gate since it is necessary to design it to stand a much greater pressure at the bottom than at the top of the gate. The same applies to water tanks of any appreciable depth — such as a ship's ballast tanks which are strength- ened towards the bottom.

Buoyancy. If we imagine that a substance is placed under water, as shewn in Fig. 6, we can see that the water will exert upon it pressure in every direction. But since the substance occupies space it is not a point and therefore the pressure in every direction will not be equal. On the upper surface A the downward pressure will be due to the vertical depth 8 A ; whilst on the lower surface the upward pressure will be due

n]

Properties of Liquids

23

to the vertical depth SB, and the side pressures will balance one another. Thus we find that the upward pressure is greater than the downward pressure.

Whether it will sink or float depends now upon the weight of the substance. If this weight is greater than the difference of . the upward and downward water pressures then the substance will sink : but if its weight is less than the difference between the upward and downward pressures it will rise to the surface and float.

D

o

' '/ "

U

*? —

\'

-A— B"-

ifference UP

\

'm

/

^Bf

- ~ -

Is'

Fig. 6

This will be true whatever the liquid may be, but of course the difference between the upward and down- ward pressures will be different if we use liquids of different density, and thus substances which would sink in one liquid might float in another.

Floating Bodies. When a body floats so that the top of it is above the surface then there is no down- ward liquid pressure upon it at all. Therefore it will float to such a depth that the upward liquid pressure upon it is just equal to its own weight. If, therefore.

24

Properties of I/iqukls

[CH.

we take some similarly shaped pieces of different sub- stances which will float, and put them on water the denser substances will sink deeper than the lighter, and the volumes of the submerged portions will be in pro- portion to the densities of the several substances.

Archimedes' experiment. Figure 7 (a) represents a spring balance on the hook of which is suspended a hollow cyhnder or bucket. Under tliis is also suspended a soUd cylinder having the same external dimensions

as the internal dimensions of the bucket and having therefore the same volume. It does not matter what this solid cyhnder is made of provided that it will sink in water. The reading of J;he spring balance is shewn. The solid cyhnder is then immersed in water — (6) — and of course the arrangement weighs less than before as shewn by the balance. The bucket is then gradually

II ] - Properties of Liquids 25

filled with water. When it is quite full (c) the balance is found to shew the same weight as it did originally.

This is known as Archimedes' experiment and it shews that the cylinder weighed less in water than in air by the weight of its own volume of water.

If the experiment be repeated using some other liquid it will be found that when the bucket is filled with that liquid the original weight will be registered on the balance.

Thus it is said that when a body is immersed in any liquid its net weight is less than its weight in air by the weight of the liquid which it displaces.

This is equivalent to saying that the difference between the downward and the upward pressures on an immersed body is equal to the weight of the liquid which the body displaces. When the body is wholly immersed the volume of displaced liquid is equal to the volume of the body.

In speaking of a ship's weight it is customary to state that its "displacement" is so many tons — a state- ment which means that the volume of the water which is displaced by the vessel when floating to its "no cargo" line would weigh that number of tons. This, of course, means that the ship and its fittings also have that weight.

Determination of Specific Gravity or Relative Density. The specific gravity of a substance — which is the ratio of the weight of any given volume of the substance to the weight of the same volume of water — may be determined in many ways. The direct methods consist simply in weighing the substance and then weighing an equal bulk of water. It is not always simple to find the volume of the substance — though this can always be done "by displacement," that is by immersing the substance in a

20 Properties of Liquida [ch.

graduated vessel ot water and noting the level of the water before and after the substance is immersed. The difference in the two volumes \v\\\ be the volume of the substance and such a volume of water can then be weighed. If the substance is one which dissolves in watesr — like copper sulphate crystals for example — then it can be placed in the graduated vessel containing some liquid in which it does not dissolve — such as alcohol in the case chosen. The difference in volume will give the volume of the crystals and an equal volume of water can then be weighed out.

The specific gravity or relative density as it is often called is the ratio

Weight of a given volume of the substance Weight of an equal volume of water

The reader will doubtless have many opportunities of making this kind of measurement and it should be unnecessary to give any details in these pages.

It should be pointed out however that these direct methods may not give very accurate results owing to the errors likely to arise in the volume measurements — especially when such volumes are small. Thus it is more usual to determine relative densities by utilising the principle of Archimedes. If a substance be weighed firstly in air and secondly suspended in a vessel of water — as shewn in Fig. 8 — the difference between these weights represents the weight of the same volume of water as the substance. Thus the specific gravity or relative density can be determined at once : and it will be recognised that the weighing can be done with great accuracy and that the w^hole measurement will take less time than a "direct" method.

ii] Projyerties of Liquids 27

If the substance is one which floats in water, then, after weighing it in air, a "sinker," of lead say, can be attached to it and a second weighing done with the sinker under water and the substance in air : then a third weighing with both sinker and substance under water. The difference between the second and third weighings will be the weight of a volume of water of the same bulk as the substance.

Fig. 8

The relative density of a Uquid is determined by weighing a solid in air, then in water and thirdly in the liquid. The difference between the first and second weighings is the weight of a volume of water equal to the volume of the substance ; and the difference be- tween the first and third weighings is the weight of the same volume of the liquid.

The relative density of a sohd soluble in water is found by weighing in air and then in a liquid in which it is not soluble. The specific gravity or relative density of this liquid must be known or found. The difference between the weighings is the weight of a volume of liquid equal to the volume of the solid. The weight of the same volume of water may then be

28

Properties of Liquids

[CH.

calculated since the relative density of the li((uid is known. From this the relative density of the soluble substance is found.

In the case of powdered substances like chalk or sand the "specific gravity bottle" is used. This is a bottle having a ground glass stopper through which a fine hole is bored. The bottle is filled with water. When the stopper is put in the excess is forced out through the hole and thus the bottle may be com- pletely filled. It is then weighed. The powdered substance is weighed and then put into the bottle. It displaces its own bulk of water. The bottle is weighed again. The specific gravity of the powder can readily be obtained from these weighings.

The Hydrometer. The hydrometer is a simple device for measuring directly the specific gravity of a liquid. It is made of glass and usually in the form shcAvn in Fig. 9. It floats in an upright position and

the thin neck has a scale on it which indicates the specific gravity of the fiquid in which it is floating. It will always float to such a depth that the weight of the

ii] Properties of Liquids 29

liquid which it displaces will be equal to its own weight. Thus in a lighter liquid it will sink further than in a heavier liquid. In the figure (a) represents the position in water, (6) in alcohol, and (c) in battery strength sulphuric acid. It is usual to have a set of hydrometers to cover a wide range of specific gravities.

Hydrometers are used in many different branches of commerce and the "scales" are usually designed to meet the particular cases. They are not usually direct reading in terms of specific gravity but in terms which meet the needs of the persons who use them. The sailor's hydrometer for example simply indicates the number of ounces above 1000 which will be the weight- of 1 cubic foot of sea water. If the hydrometer sinks to 25 it means that 1 cubic foot of that water will weigh 1025 ounces. The brewer's hydrometer has a scale which is used in conjunction with a specially compiled set of tables. And even some of the ordinary hydro- meters have scales which require the use of some constant or some empirical formula in order to obtain the specific gravity of the liquid in which they are immersed. Of such kinds perhaps Beaume's and Twaddell's are best known.

Pumps. The action of the simple pumps should not require any detailed explanation after the foregoing discussions. The diagrams shewn should be nearly sufficient.

Fig. 10 illustrates a simple lift pump. In the pump a piston B can be moved up and down in a cylinder. In the base of the cylinder is a valve — shewn in the diagram as a flap — which will open if the pressure below is greater than that above and shut if it is less. In the piston 5 is a similar valve which opens and shuts under

;}()

Properties of Liiiuuh

[CH.

similar conditions. The cylinder base is connected to the wat«r through a fall pipe.

When the piston is raised the effect is to expand the air between A and B and so lower the pressure there. This shuts the valve in B and the water from the well is forced up the pipe P by the excess of the atmospheric pressure over the cylinder pressure. Thus the cyhnder becomes filled. The piston is then pushed down. This sliuts the valve A and opens B so that

Fig. 10

Fig. 11

the water is forced to the top of the piston. The piston is raised again and with it, of course, the water above it which comes out of the outlet O. At the same time the previous action is going on below the piston.

Fig. 1 1 illustrates a force pump in which the water is forced out of the outlet under pressure. This is the tj^pe of pump used for fire-engine work, garden pumps, etc.

ii] Properties of Liquids 3 1

The piston B has no valve. When it is Hfted valve A is opened and C is closed. Water enters the pump cylinder. On the downward stroke A is closed and the water is forced through C into the chamber F. As the water rises in this chamber above the lower level of the outlet pipe it will compress the air until ultimately the pressure will be sufficient to force the water through 0 in a more or less continuous stream.

It should be remembered that since pressure is dis- tributed equally in every direction in a liquid a force pump having a small cylinder can nevertheless be used to produce a total enormous pressure. For example if a steam boiler is to be tested for pressure, the test employed is a "water test" in which the boiler is filled completely with water. A hand pump capable of generating 300 lbs. per sq. inch pressure is then coupled to the boiler and the pump is operated. This pressure is communicated to the boiler and the water will exert an outward pressure of 300 lbs. per sq. inch on every square inch of the boiler. Any leak will shew itself: and in the event of the boiler breaking down no hurt is likely to be caused to those conducting the test.

It is in the same way that the hydraulic press, the hydraulic ram and hydraulic jack are operated.

The reader possibly knows that the feed water pump of a steam boiler pumps water into the boiler against the steam pressure. If the steam pressure is 150 lbs. per sq. inch then the feed water must be pumped in at a greater pressure. This can be done with quite small pumps, for the pressure which can be generated and distributed does not depend upon the capacity of the cylinder.

32 Properties of Lltjuids [cji.

Capillarity. If we examine the surface of water in a glass vessel we notice that all round the edge next to the glass the water is curved upwards. If we dip a piece of clean glass tube into the water we notice the same curving against the wall of the tube both inside and outside. If the tube has a fine bore we also notice — perhaps to our surprise — that the water rises inside this tube to a greater height than the water outside. If we use tubes of different internal diameters we shall find that the water rises to a greater height in the fine bored tubes than in the large bores. Because of this fact — that the phenomenon is shewn best with tubes as fine as hairs — it is called capillarity.

If we use mercury instead of water we observe a reversed formation of the surface, and the mercury in the tube will be depressed below the surface of that outside. Again as We use finer and finer tubes the depression wiU become correspondingly greater. Fig. 12 illustrates the surface formations in the two cases. Fig. 13 shews what happens when these liquids are poured into U -tubes having a thick and a thin limb — the thin limb being a capillary tube^.

Mercury does not "wet" glass and if any hquid be placed in a vessel of material which it does not wet its surface would be formed similarly to the mercury in glass. If a pencil of paraffin wax be dipped into water it will be found that the edge of the water against the wax is turned down. If a piece of clean zinc be dipped into mercury the edge_of the mercury near to the zinc will be curved upwards — just like water against glass.

There are many illustrations of capillary action.

' The size of the capillary tube is exaggerated for the purpose of the diagram.

ii] Properties of Liquids 33

There is the feeding of a lamp -flame with oil : the wetting of a whole towel when one end is left in

Water Mercury

Fig. 12

water : the absorption of ink by blotting paper : the absorption of water by wood and the consequent swelling of the wood.

Water Mercury

Fig. 13

Surface Tension. The surface of any liquid acts more or less like a stretched membrane. A needle can be floated on water if it first be rested on a cigarette

P.Y. 3

34 Properties of Liquids [CH.

paper which N\ill ultimately sink, leaving the needle resting in a little depression on the surface — but actually not making any contact with the water. Many insects walk on the surface of water. A camel- hair brush under water has its hairs projecting in all directions, but when it is withdrawn all the hairs are drawn together as though they were in a fine india- rubber sheath. The formation of a drop of water shews the same thing — how the water seems to be held in a flexible skin. This skin is under tension and endeavouring to contract. Hence we find rain drops are spherical : drops of water run off a duck's back like hailstones off an umbrella: lead shot is made by "raining" molten lead from the top of a tall tower into a water vat at the bottom.

Different liquids have different surface tensions which can be determined or compared either by observing the heights to which they rise in capillary tubes of equal diameter, allowances being made for the different densities of the liquids, or by a direct weighing method. This consists in suspending a thin plate of glass vertically from one arm of a balance and adjusting the balance. A vessel of water is then placed beneath the glass and gradually raised until the water just touches the lower edge — when the surface tension pulls down the balance. Weights are placed on the other pan until the glass is brought up again so that its lower edge just touches the water or whatever Uquid is being tested.

Diffusion. If we place some coloured salt solution at the bottom of a vessel of water — and we can do it very easily by means of a pipette — we shall find quite a sharp dividing line between the heavier salt solution and the lighter water. But if we leave them undisturbed

ii] Properties of Liquids 35

we shall find that very gradually some of the heavy liquid will have come to the top and some of the lighter water will have gone to the bottom and that eventually the Kquids will become mixed. This gradual intermingling — done apparently against the laws of gravity — is called dijfusion.

Diffusion takes place more readily between gases than between liquids, and every gas can diffuse into every other gas : this cannot be said of Uquids.

In the case of gases it is impossible to keep them separated one upon another — like oil upon water. This is fortunate for us, because if gases arranged themselves layer upon layer with the heaviest at the bottom and the lightest at the top our atmosphere would consist of successive layers of carbonic acid gas, oxygen, nitrogen, water vapour and ammonia. Animal life would be impossible. As it is however gases diffuse so readily that they are all intimately mixed — and even in the immediate neighbourhood of an oxygen manufactory which takes its oxygen from the atmosphere there is no sign of a scarcity of oxygen; this is due to the rapid diffusion which takes place.

Viscosity. Some liquids are more viscous than others. It is easier to swallow water than castor oil, not so much because of any special or objectionable flavour but because of the slow dehberate manner in which the oil trickles down the gullet. The oil is said to be viscous ; and treacle, honey and thick oils have this property of viscosity to a great degree. It may be said to be due to frictional forces between adjacent layers.

Liquids which flow readily — like water or alcohol or petrol — are called mobile liquids.

3—2

30 Proper ticK of Liquids [oh. ii

The viscosity of a liquid is usually lowered by an increase in temperature : so much so that when super- heated steam is used in a steam engine the question of lubrication becomes more difficult.

Viscosity of different liquids may be compared by finding the rate at which they may be discharged through equal tubes under equal pressures.

EXAMPLES

1. What is the total pressure on the base of a rectangular tank full of water, the internal dimensions being 6' deep, 8' long and 4' wide? Also find the total pressure and the average pressure in lbs. per square inch on each side of the tank.

2. A diver is at a mean depth of 30 feet below the surface of the sea. What must be the least pressure of the air supplied to him in lbs. per square inch so that he does not feel the pressure of the water upon his diving suit? The relative density of sea water is 1025.

3. A substance weighs 256 grammes in air and its relative density or specific gravity is 8-4. What would it weigh if immersed in water ? What would it weigh in a liquid of specific gravity 1-25 ?

4. A substance weighs 7-6 ozs. in air and 6-95 ozs. in water. What is its specific gravity ? What is its volume in cubic inches ?

5. A substance weighs 32-6 grammes in air and 26 grammes in a liquid whose specific gravity is 0-84. What is the specific gravity of the substance and what is its volume ?

6. Four lbs. of cork of specific gravity 0-18 are securely fastened to 15 lbs. of lead of specific gravity 11-4. Will they sink or float when immersed in water ?

CHAPTER III

PROPERTIES OF GASES

As we have already seen a gas is a portion of matter which has no rigidity and which is readily compressed. It has neither definite shape nor definite volume, for a given mass of it may be made to occupy various volumes at will by varying the pressure to which it is subjected.

We have already seen that gases have weight and it is the weight of the air surrounding the earth which causes the pressure commonly called the atmospheric pressure. It is that same weight which causes the air to hang round the earth instead of distributing itself through the vast vacuous spaces which nature is said to abhor. As the reader probably knows, the belt of air about the earth does not extend to the moon — as was supposed to be the case in the early part of the seventeenth century— but is only a few miles deep. ,The total weight of this belt of air on the earth's surface is enormous, and if the reader would like to know exactly how much it is he can calculate it from the fact that the pressure of the air is, on the average, 14* 7 lbs. to the square inch. He has therefore only to calculate the number of square inches on the surface of the earth and multiply this by 14-7 and he will have the total weight of the air in pounds.

When a gas is enclosed in any space it exerts pressure

iMi Properties of GascH [c'H.

ill every direction. Moreover it exerts pressure equally in every direction. One of the simplest illustrations which can be offered of the truth of this stat-ement is that of the soap bubble. It matters not how we blow into the bubble, or what manner of pipe we use, the bubble is beautifully spherical. If the pressure of the gas both inside and outside the soap film were not equal in every direction then clearly the bubble' would not be spherical in form.

If we construct a cylinder — as shewn diagiammati- cally in Fig. 14 — and provide it" with a number of pressure gauges, then when a piston is forced into the

Fig. 14

cylinder it will be seen that all the gauges indicate the same pressure at a given moment. On the other hand we know that if the cyhnder were filled with a solid — like steel for example — and pressure was applied to the piston there would be no pressure exerted on the sides of the cylinder: it would only be exerted on the end. If we filled the cylinder with water we should find that it exerted pressure in all directions equally.

The fact that a gas exerts pressure equally in all directions accounts for our unconsciousness of the existence of atmospheric pressure. It would be im- possible for us to hold our arms out at length if the

in] Properties of Gases 39

atmospheric pressure of 14-7 lbs. per square inch were only acting downwards. The air would indeed be a burden to us.

A simple experiment illustrating the magnitude of this pressure may be made by exhausting the air from the inside of a tin can. The surest and simplest way of doing this is to put a little water inside the can and boil it. When steam is coming freely from the opening remove the flame, cork up the can, and plunge it into a vessel of cold water. The can will immediately collapse. The explanation is that the air was driven out of the can by the steam, and that the cold water condensed the steam thus reducing the pressure inside the can to practically nothing. The pressure of the air outside acting in every direction upon the can is sufficient to crush it. It is probably known to many readers how in certain engineering operations — tunnel- ling under a river for example— the workmen work in a high pressure space in a special "shield." The pressure of the air in this shield is considerably higher than that of the atmosphere outside and the men have to pass through a sort of air lock in which the pressure is gradually raised to that inside the shield or gradually lowered to that of the atmosphere according to the direction in which the men are going. The change of pressure is decidedly unpleasant unless it is done very gradually so that the pressure inside the body may never differ sensibly from that outside.

It is well known that if a piece of paper be placed over the top of a tumbler filled with water the whole may be held in an inverted position and the water will not force the paper away. In this case the downward pressure on the paper is represented by the weight of

4()

Properties of Gases

[CH.

the water iji the tumbler and the upward pressure is the atmospheric pressure of 14-7 lbs. to the square inch. There is no downward atmospheric pressure on the paper because there is no air in the tumbler. Unless the tumbler be 34 feet or more in length the upward atmospheric pressure will be greater than the downward pressure of the water in th(> tuniV)ler : hoiu-(^ it will not run out.

If a glass tube of about 3G inches length be arranged as shewn in Fig. 15 so that one end dips under some mercury and the other end is connected to a vacuum

To Vacuum pump

Pig. 15

pump the mercury will rise in the tube as the vacuum improves until finally it reaches about 30 inches above the mercury in the lower vessel. Beyond this it will not rise however good the vacuum may be. If the experiment be repeated with other liquids — and in such a case the tube should be 40 feet long — it will be found that water will rise to about 34 feet, glycerine to about 30 feet, and so on. But in every case the height to which the liquid rises will be such that it will produce

IIIJ

Properties of Gases

41

a pressure of about 14-7 lbs. per square inch at the bottom of the cohimn — which is to say that the Hquid will rise up to such a height that it produces a down- ward pressure equal to that of the atmosphere.

The Barometer. It is on this principle that we usually measure atmospheric pressure, the instrument used being called a barometer. To construct a barometer a glass tube of 36 inches length having a fairly thick wall and a bore of about | inch is sealed at one end and filled with clean mercury. Care must be taken that no air bubbles or water vapour are left in ; and to this end the tube should be thoroughly cleaned and dried before filling. A finger is then placed over the end and the tube is inverted and its lower end placed in a dish or cistern of mercury. The finger is then removed and the mercury will fall a little in the tube — as shewn in Fig. 16 (a). Since there is no air in the

Fig. 16

tube the column of mercury will adjust itself to such a height that its downward pressure is the same as that of the atmosphere. The "height" of the barometer

42 Properties of Gases [v\\.

is the vertical difference of level between the mercury in the tube and the mercury in the cistern. If the tube be tilted as shewn in Fig. 16 (6) or made in the form shewn in Fig. 16 (c) the mercury will adjust itself so that the vertical difference of level is the same as in the straight vertical tube.

Standard Barometer. In the usual standard pattern of mercury barometer the cistern is provided with a plunger, worked by means of a screw, which can be adjusted so that the level of the mercury in the cistern coincides with the zero mark of the scale of inches and centimetres. This adjustment must always be made before the height of the barometer is read. It will be clear that unless some arrangement of this kind is provided a rise in the barometer will draw some mercury out of the cistern and the level vdW be below the zero of the scale ; whilst a fall in the mercury will raise the cistern level above the zero of the scale. In the usual domestic pattern this is compensated for in the marking of the scale : and it will be found that the distances marked off are shghtly less than true inches. It is of course cheaper to do this than to provide a special cistern.

Boyle's Law. The relationship between the volvmae which a given mass of a gas occupies and the pressure to which it is subjected is expressed in a law known as Boyle's law. This states that the volume of a given mass of a gas, kept at constant temperature, varies inversely as the pressure to which it is subjected.

Most of us learned jgomething about this law when we played with popguns. We learned -that as we decreased the volume of the air in the barrel of the gun by pushing in the plunger we increased the pressure on

Ill

Properties of Gases

43

the cork and on the plunger until finally the cork was blown out. We found that the plunger was harder to push as it got further into the barrel and in learning this we had got the main idea of Boyle's law, that if we increase pressure we decrease volume. What we had not learnt was the exact relationship between the two, namely that the one varies inversely as the other. Thus if the pressure be doubled the volume will be halved : if the pressure be increased seven times the volume will be reduced to one-seventh and so on.

This law may be experimentally verified by means of the apparatus shewn in Fig. 17, in which we have

/\

I

Fig. 17

two tubes L and R connected by some rubber tubing. L is sealed at the top and is graduated in cubic centi- metres or inches or any other scale of volume. R is

44 Proper tHx of Goscs [CH.

open to the atmosphere and is arranged so that it can be raised or lowered. A certain volume of dry air (or any other dry gas) is enclosed in L by means of mercury and the volume can be read off on the scale. By raising or lowering R the pressure and volume of the gas in L can be changed.

If the side R be adjusted so that the level of the mercury is the same in both tubes then it follows that the pressure is the same also. But the pressure on the surface of the mercury in R is the atmospheric pressure and therefore if we read the height of the barometer we know the pressure of the gas in L and we can read the volume on the volume scale. If R be now raised, as shewn in the top diagram on the right, so that the level of its mercury is above the level of the mercury in the tube L, then it follows that the pressure of the gas in L is greater than the atmospheric pressure by the pressure represented by a column of mercury of length AB — since it can support this column of mercury in addition to the atmospheric pressiire. Therefore the new pressure is the atmospheric pressure in inches or cms. plus the difference in the level of the mercury in the two limbs also in inches or cms. as the case may be. If, on the other hand, the limb R be lowered so that its mercury is below that in L it follows now that the atmospheric pressure is greater than that in L by an amount represented by the difference in level AB, so that the pressure of the gas in L is the atmospheric pressure minus the difference in level AB.

The following are some results obtained with this apparatus :

Ill]

Properdes qf Gases

45

Volume

Heiglit of

Difference of

1 Pressure of

.Pres-

of gas

barometer

level AB

gas in L in cms.

sure X

in L

in cms.

in cms.

of mercury

Volume

8

75-8

+ 53

128-8

1030

11

75-8

+ 17-7

93-5

1028

12

75-8

+ 9-6

i 85-4

1024

15

75-8

- 71

68-7

1030

16

75-8

- 11-4

64-4

1030

17

75-8

- 15-2

60-6

1030

18

75-8

- 18-4

57-4

1033

24

75-8

- 32-8

43

1032

In the last column of the tabulated results the product of the pressure and the volume is given and it is seen that this product is practically the same right down the column. When one quantity varies inversely as another and a number of results are taken under equal conditions then it will always be found that the product of the two quantities is constant.

If Pj represents the pressure when the volume is Fi and P^ represents it when the volume is Fg then Boyle's law may be expressed

V, Pi-

That is to say the ratio of the volumes is equal to the inverse of the ratio of the pressures under equal circumstances.

Therefore ^i^i==^2^2-

Hence the fact that our last column is practically constant js an experimental verification of the law.

The relationship between the volume and pressure may also be plotted as a graph. Fig. 18 shews the graph given by the results above. The form of this curve is known mathematically as a rectangular hyperbola.

40

Properties of Gases

[CH.

It will be seen later that Boyle's law is not universally true, though for dry gases it can be regarded as suffi- ciently true for all practical purposes.

25 20

15

10

5

1

X

50

150

200

Fig. 18.

100 Pressure Curve shewing relation of volume and pressure of air at constant temperature.

Airships. The principle of Archimedes is as true for gases as it is for liquids. Any object weighs less in air than it would do in a vacuum by the weight of its own volume of air.' It also weighs less near to the ground where the air is dense than it would do at a higher level.

Ill] Properties of Gases 47

A balloon or any other lighter-than-air ship is filled with a gas lighter than air and is made of such a volume that the weight of air which it displaces is greater than its own weight. It is thus buoyed up and will rise to a height such that the weight of air displaced at that height is equal to weight of airship and contents. To ascend the volume of air displaced must either be in- creased (as in the Zeppelin type) or the weight must be decreased by dropping ballast. To descend the volume of air displaced must be decreased.

EXAMPLES

1. A certain mass of aii- has a volume of 12 cubic feet when there is a pressure of 14-7 lbs. per square inch (1 atmosphere) acting upon it: what will its volume be when the pressure is [a) 10 lbs., {h) 17-5 lbs. per square inch?

2. A steel oxygen cylinder has an internal volume of 3 cubic feet. It is filled with oxygen at a pressure of 120 lbs. per square inch. What would be the volume of the gas at atmospheric pressure ?

3. If a mercury barometer reading was 29-4 inches, what would be the reading of a glycerine barometer at the same time- — the specific gravity of glycerine being 1-21 and that of mercury 13-6?

4. Plot the graph shewn in Fig. 18 and extend it on each side to shew the volume changes between the pressures of 20 and 200.

5. A balloon on the ground where the atmospheric pressure is 14-7 lbs. per square inch displaces 30,000 cubic feet of air. What volume will it displace when at such a height that the atmospheric pressure is 12 lbs. ?

6. When a certain steam boiler is working at a pressure of 120 lbs. per square inch it is capable of discharging 20 lbs. of steam per minute. If the pressure be worked up to 150 lbs. per square inch and maintained there what would be the possible discharge rate ?

7. A cylindrical steel cylinder is 5 feet long and 8 inches in- ternal diameter and is filled with "Poison gas" at a pressure of 100 lbs. per square inch. What space would this gas occupy when let out into the air when the barometer reads 30 inches of mercury ?

CHAPTER IV

FORCE, WORK AND ENERGY

Work. We buy coal, not for its own sake, but for the heal which we can get out of it. We buy gas from the gas company for the light which we can get from it in burning. Neither heat nor light can be regarded as matter : they have no weight and no other property which we associate with matter.

We classify them as forms of energy and we define energy as the capabiUty of doing work.

For scientific purposes we have a definite meaning for the word work, and it is restricted to the production of motion of matter. We say that when a force acting upon a body produces motion then work has been done. Unless motion is produced however no work is done.

Force. In order to produce motion we must apply force. We have seen already that weight is a force ; we possess a system for measuring weights and we can therefore measure our forces in terms of pounds weight, or grammes weight or any other units of weight that we care to use. We can also indicate these forces by means of spring balances so that we can be quite independent of the force of gravity.

If we raise a bucket of water vertically upwards we shall have to apply a force which, it can be seen, will be equal to the total weight of the bucket and its contents. If we just haul it along the ground without

CH. iv] Force, Work and Energy 49

lifting it the force which we shall have to apply will depend entirely upon the surface of that ground. If this is very smooth — like ice — very little force will be needed to haul the bucket along ; but if the surface be rough and gritty then the force required might be considerable.

We can take a better illustration from railway traction. If we have to raise a truck bodily off the rails then we must apply a force equal to the total weight : but if we have to move it along the rails then it is only necessary to apply a force sufficient to over- come the friction of the bearings and the rails, and that force is about 10 to 15 lbs. for every ton which the truck and its contents weigh. Thus if the truck and its contents weighed 10 tons then the force to lift it vertically upwards would be 10 tons or 22,400 lbs. : but the force necessary to move it along the rails would only be 100 — 150 lbs. according to the quality of the truck and the track.

Now work is measured by the force required to produce the motion and by the amount of movement produced ; that is to say by the product of the force producing the motion and the distance through which the object moves in the direction in which the force is being applied.

Units of Force and Work. Clearly a unit of work will be done when a unit of force produces motion through a unit of length in its own direction. It follows therefore that we may have many different units. On the British system the unit most commonly used is the Foot-Pound — namely the work done when a force of one pound produces motion to the extent of one foot in its own direction.

p. Y. 4

'){) Force, Woric and Energy [ch.

In scientific work the units of force chiefly used differ from the *' weights" which have been given. A unit of force is defined as tliat force which acting for a unit of time upon a unit of mass produces a unit change of velocity. For example it is found that if a force of 7|.V.j lbs. weight be apphed to a mass of 1 lb. mass which is free to move without friction, it will move and its velocity will increase by 1 foot per second every second. Therefore the unit of force according to this definition is ~~,, lbs. weight. This is called a Poundal.

Similarly it is found that a force of tj^t gramme weight will cause the velocity of a mass of 1 gramme to increase by 1 centimetre per second every second. Thus the metric unit of force is y^y gramme weight. This is called a Dyne.

Returning to our units of work again we see that the true unit of work on the British system would be a foot-pounial, which is ^^ of the foot-pound ; and on the metric system we have the centimetre-dyne which is called an erg. This is a very small quantity of work, and the practical unit of work on the c.G.s. system is a multiple of the erg, namely 10,000,000 ergs, and this unit is called a Joule.

1 joule is equivalent to 0-737 foot-pound. This is the electrical engineer's unit of work.

Mechanical engineers generally prefer to use one pound weight as a unit of force and one foot-pound as the unit of work. This means that the engineer's unit of mass must be correspondingly increased in order to meet the conceptionjaf a unit of force being that force which would produce a change of velocity of 1 foot per sec. in one second when acting on a U7iit mass. A force of 1 lb. weight would produce a change of 32-2

iv] Force, Woric and Energy 51

feet per sec. in one second on a mass of 1 lb. mass : but if the mass were increased to 32-2 lbs. mass the change of velocity per second produced by a force of 1 lb. weight would only be 1 foot per sec. Therefore the engineer's unit of force is the pound weight and the unit of mass is 32-2 lbs. No name has been given to this although the remarkable word slug was once suggested.

This Ust of units is very dull and uninteresting but of very great importance. A student who slurs these over is storing up trouble for himself, for there can be no doubt that the man who understands all his units will have little or no trouble with the various numerical problems of his subjects.

Examples of work. We may briefly illustrate the use of these units. If a railway truck requires a force of 100 lbs. to pull it along so that it is just moving against the friction then the work required will be 100 foot-lbs. for every foot along which it is moved. Let us find out how many ergs and joules this is equiva- lent to. Since there are 453-6 grammes to the pound, the force = 453-6 x 100 grammes weight; and since there are 981 dynes of force to the gramme weight the force in dynes = 453-6 x 100 x 981.

Further since there are 30-48 centimetres to the foot the work done in centimetre -dynes, i.e. in ergs, will be 453-6 X 100 X 981 x 30-48 or 1,356,303,916 ergs. And since there are 10' ergs to 1 joule the work done in joules will be 13 5* 63 joules.

If work is done by a force which varies in magnitude, then the product of the average force and the distance through which it is applied will give the measure of that work. The measurement of the work done on the

4—2

52 ■ Force^ Work and Energy [ch.

piston of a steam engine during its motion along the cylinder is an example of this kind, jand the indicator diagram represents how the force is changing for each position of the piston. From the diagram the average force can be determined (see Chapter XIII).

Energy. We say that a body has energy when it is capable of doing work and therefore we measure its energy by the number of units of work it can do.

For example, the weight of an eight-day clock when wound up to the top is capable of doing a certain amount of work in falling gradually to its lowest position. If the weight weighs 7 lbs. and the distance between its highest and lowest position is 4 feet then when wound it possesses 28 foot-lbs, of energy which it can give out to keep the clock going. When it has fallen half-way it only possesses 14 foot-lbs. of clock energy — the other 14 having been given up.

There are two general divisions of energy. Some bodies, hke the clock weight, possess energy on account of their position or state. A compressed spring, a coiled-up watch spring, a sprung bow, an elevated pile- driver, a stone on the edge of a cliff and some water in a high reservoir are examples of things possessing energy because of their condition, position or state. We say that these things have potential energy.

Other bodies are capable of doing work because of their motion. A flying bullet, a falling stone, the water of a waterfall, the steam forced from a high pressure boiler, the wind, a hammer head just at the moment of impact, are examples of things possessing energy due to their motion. We say that these have kinetic energy.

The energy of a body is capable of being changed from potential to kinetic and vice versa. Fig. 19 (a)

IV]

Force, Work and Energy

53

represents a pile driver: position A shews the driver at rest at its highest position where its energy is all potential : position B represents it moving downwards towards the pile, and though its potential energy must be less than it was at A yet it now has kinetic energy due to its motion : position G represents it at the moment of impact, and here its potential energy in relation to the pile is zero but its kinetic energy is greater than it was at B since it has gained speed.

h II

1 1 I I I I I i I I I I I I I I I I I

E F

(a) (b)

Fig. 19

Fig. 19 (6) represents a pendulum swinging between extreme positions of D and G. At the positions D and G it is at rest at its highest position and its energy is all potential. At F it is at its lowest position and its pendulum energy is all kinetic. At E its energy is partly potential and partly kinetic.

The reader will learn that in all these cases the sum of the potential and kinetic energies at any moment is a constant quantity; and that what a body loses in potential energy it gains in kinetic energy.

.')4 rurct, WinL nuil Entiijij [cm.

Principle of the Conservation of Energy. Many ex- periineiits liave heoii pcrlorinod in comparatively recent times which go to shew that though we can alter the jorm of the energy of a body yet we cannot destroy energy nor yet can we create it. We shall deal with some of these experiments at a later stage, but it should be made clear to the reader now that this is regarded as an estabHshed fact and that it is practically the funda- mental basis of modern science. It is known as the principle of the conservation of energy and it is exactly parallel to the principle that matter can neither be created nor destroyed though it can be changed in form and condition.

The reader will ask what happens to the energy of the pile driver when the driver has come to rest on the pile head ? It is found that it has been changed into another form — a form which we call Hmi. With the aid of heat mechanical work can be done and it has been shewn that the amount of mechanical work which a given "quantity of heat" can do is such that if this same amount of mechanical work be converted into heat it will produce in turn the same "quantity of heat" as that with which we started. And further, in whatever way we do work which produces heat — whether by friction or by hammering or by boring or by percussion — we always get the same " quantity of heat" if we do the same amount of work. This is discussed in detail in Chapter XIII.

In the same way^heat energy Qan be converted to light energy. Heat energy can also be converted to electrical energy, mechanical energy can be converted to electrical energy which in turn can be converted to heat or to light or to mechanical energy again. In fact

Tv] Force, Woi'h and Energy 55

it. is just that "flexibility" of electrical energy which makes it of such use to mankind, for it is so easy to transmit from one place to another and it is so easily changed to whatever form or forms we desire. Then in coal we have a store of chemical energy which changes to heat in burning ; the heat is given to water and pro- duces steam at a high pressure charged as it were with potential energy ; the steam is liberated and its kinetic energy is given up to the piston of an engine ; the kinetic energy of the engine is transmitted to the dynamo and converted to electrical energy ; the electrical energy is transmitted to where it is needed and there transformed to any form we wish — to heat, to light, to chemical energy in secondary cells and in chemical manufacturing process and to mechanical energy in motors. But all this energy has come from the boiler furnace ; we have not made any ; we have not destroyed any ; but we may possibly have wasted a considerable quantity. We have not used all the heat given by the coal — much has gone up the chimney so to speak ; we have produced heat at all our bearings because we cannot make them mechanically perfect and frictionless,'and so the energy necessary to overcome that friction has been changed to heat.

We may sum up then by saying that energy like matter can neither be created nor destroyed but that it can be changed from any one form to any other form of which it is susceptible.

Power. In scientific work this word has a very restricted meaning and one which differs considerably from its meaning in common usage. By power we mean the rate at which work is done. 20 foot-lbs. of work may be done in a second or in an hour and though

.")G Force, Work and Energy [ch. iv

the actual ^^'ork done \\ ill be the same in each case yet the rate of working will be very different. The unit of power would naturally be the rate of working when a unit of work is done in a unit of time. In practice, engineers take as a unit of power 550 foot-lbs. of work per second which is called 1 horse-power. This is equivalent to 33,000 foot-lbs. per minute. The elec- trical engineer's unit of power is 1 joule per second which is called a ivatt. 1000 watts or 1000 joules per second is called a Hlowatt and this is more generally used in heavy electrical engineering. 1 horse-power is equiva- lent to 746 watts.

It might be well to point out here that a 1 horse- power motor might be constructed to work at high speed so that it could, for example, haul up a load of 1 lb. through 550 feet in a second, whilst another 1 horse-power motor could haul up 550 lbs. through 1 foot in a second. Thus a mere knowledge of the horse-power does not give ua any idea of the hauling capacity of the motor or engine and it is entirely wrong to imagine that a 1 horse -power motor can necessarily pull with the same puU us that which can be exerted by an average horse.

The reader can ask himself what is the object of the gear box of a motor car.

EXAMPLES

1. How much work would be done in pumping 120,000 gallons of water from a depth of 22 feet ? If this work were done in 2 hours what would be the rate of working (a) in foot-lbs. per minute, (b) in horse- power? ^

2. How many ergs of work are equivalent to 1 foot-lb. ? (There are 45.3-6 grammes per lb. and 2-54 cms. to the inch.)

How many joules of work is this equivalent to and if the work was done in l/5th sec. what would be the rate of working in watts?

CHAPTER V

HEAT AND TEMPERATURE

It may be well to begin by saying that we do not know what heat really is. All we can say with any degree of definiteness is that heat is an agent which produces certain effects. We can study the nature of these effects and the conditions under which they may be produced and their application generally for the benefit of mankind. A moment's reflection will shew that we need not necessarily know the precise nature of this thing which we call heat, although, on the other hand, we can see that such knowledge might help us considerably both in the production and use of this most valuable agent.

We know that heat can produce certain effects. Our first knowledge is of its comforting effects upon our person and of its chemical effects upon our food. And as our vision grows more extended we become conscious of its effects upon life in both the animal and vegetable worlds. Then we find how it can change the physical state of matter from solid to liquid and from liquid to gas. Then again we begin to realise that it is an agent which can do work for us. We think of the steam engine and reflect that after all it is the burning of the fuel which yields us all the energy ; and further knowledge shews us that in the gas engine, the oil

i)H Hent nmf Temjterdtnrv [CH.

engine and the petrol engine, combustion and the pro- duction of heat give us the source of all their energy of motion. How important then it is that we should know as much as possible about the various effects which heat can produce and the various methods of producing and using it.

Production of Heat. We have already seen that energy can shew itself in many different forms, and that one of these forms is heat. We have reahsed that energy like matter can be changed from one form to another, and that it can neither be created not yet destroyed. It follows therefore that whenever we produce heat it is at the expense of an equivalent amount of energy which was previously existing in some other form.

The chief method of production is by the expendi- ture of chemical energy. All forms of burning or com- bustion are examples of this, from the combustion of that great mass which we call the sun down to the burning of the humble match. If we bum a given mass of anything — coal or candle — and keep all the residue we shall find the mass of matter the 'same as before, but that mass has no longer the energy which it had before combustion. The heat was obtained not at the expense of any of the matter or stuff but at the expense of its chemical energy — that mysterious weight- less attribute of the coals or candles for which we really pay when we buy them. We do not really want the coal as such when we buy it: we want the chemical energy which it contains and which we can change to heat energy whenever we desire to do so. The same statement applies to any other kind of fuel and to all those fearsome mixtures termed explosives.

v] Heat and Temperature 59

Further it is probably known to most readers that heat can be produced by chemical changes without combustion. If some water be added to strong sulphuric acid heat will be produced at once, and con- sequently great care must be taken in the dilution of acids. Further everyone knows how heat is developed in a haystack if the hay be stacked before it is dry.

The mechanical energy of motion may be changed into heat. Whenever there is any kind of resistance to motion — that is to say any kind of friction — heat is developed in direct proportion to the amount of energy necessary to overcome that friction. Such heat is, as a general rule, waste energy ; but as friction is always present the loss is unavoidable. An engine driver tests the bearings of his engine by feeling them. Bad bearings become unduly heated, and the increase in warmth serves as a danger signal. The striking of a match is an example of the useful conversion of mechanical to heat energy. The old flint and tinder, and the yet older rubbing of dry sticks together are similar examples. "Shooting stars" are examples of the heat produced by the resistance of the air to bodies falling through it at an enormous speed. The melting of a rifle bullet on striking a steel target affords another example of the changing of mechanical energy to heat.

Electrical energy can also be converted to the form of heat and every reader knows something about electric lighting and heating.

In short whenever work is done without producing its equivalent in some other form of energy the balance is shewn in the form of heat..

Temperature. We know that a reservoir of water is capable of doing work and that such work can only

60 Heat and Temperature [ch.

be done by the motion of some of the water. It can do work, for example, by a downflow to a water-turbine and we know that the amoimt of work which the reservoir can do depends upon the quantity of water it contains and the height of the reservoir above the ivater -turbine. That is to say the energy of the reservoir is measured by the product of the mass of water arid the height above the turbine, and we coukl get the same energy out of a reservoir at half the height if it held twice as much water.

Let us imagine that any furnace or source of heat is a sort of reservoir of heat energy — the energy de- pending upon some quantity we will call heat and upon some kind of height which we will call temperature or heat-level.

The analogy between this reservoir and the water reservoir will hold good for most things but it ought to be borne in mind that it is only an analogy and that we are taking a considerable licence in comparing heat to water. But just as we say that water will always flow from a reservoir at a higher level to one at a lower level quite irrespective of the size or shape or quantity of water or amount of energy in those reservoirs, so also may we say that heat is only transmitted from a body at a higher temperature to one at a lower temperature whatever may be the other differences between those bodies.

We may thus take it that temperature is a sort of level of heat as different from the agent heat itself as height or level is different from water. Nobody would confuse a reservoir of water with its height, yet most people confuse heat and temperature.

Measurement of Temperature. It will be necessary

v] Heat and Temperature 61

to measure temperatures or differences in temperature if we are going to make any really valuable investi- gations into the effects of heat upon bodies. Our senses enable -us to form a rough estimate of tempera- ture such as saying that this body is hotter (i.e. at a higher temperature and not necessarily containing more heat energy) than that. But our senses are not reliable, for they can lead us into the declaration that one thing is hotter than another when they are actually at the same temperature. An example of this may be fur- nished at any moment, for if we go into any room which has been without a fire for some time, having therefore a uniform temperature or heat level all over, and touch various articles such as the fender or curb, the hearth- rug and a table leg, we shall find that they all appear to have different temperatures. The explanation of this lies simply in the fact that the articles conduct heat to or from the body at different rates and so produce different sensations.

Temperature is measured by means of a thermometer which depends for its action upon the fact that when heat is given to matter it generally produces an increase in volume.

Let a glass flask be taken and filled with water (or any other liquid) and provided with a cork and tube so that the water rises to some height A in the tube, as shewn in Fig. 20. If now some hot water be poured over the flask it will be noticed that at first the water drops to a position such as B but soon rises again to such levels as C and D. We might perhaps imagine that water there- fore contracts for a moment when heated : but if we heat the water from within — by means of a small coil of wire through which a current of electricity can be passed —

()2

Heat and Temperature

CH.

we shall find that there is no initial dnj]). 11 we bend a piece of glass tube or rod into the fonn of a triangle and bring the two sides together at the apex so that they can just grip a coin — as shewn in Fig. 21 — and then heat the base we shall find that glass expands when heated ; this will be shewn by the coin dropping from the apex of the triangle. We therefore conclude that the dropping of the water in the first instance — when the hot water was poured over the fiask — ^was due to the

Fig. 21

Fig. 20

glass receiving the heat first and expanding, thus having a larger volume. But when the heat got through to the water inside then that expanded too, and since it ultimately went above its original mark A we conclude

v] Heat and Temperature 63

that water expands more than glass does. As a matter of fact liquids in general expand more than solids.

Now if we put this flask into vessels of water at different temperatures we shall find that the water in the tube will set at a different level for each tempera- ture.

This furnishes us with the basis of temperature measurement. We could mark a scale off in any way we desired and it would be sufficient perhaps for our purpose — ^but if everybody had his own scale of tempera- ture we could hardly make any progress. What the scale is really does not matter ; but it is of first import- ance that we should all use the same. The well-known case of the bricklayer's labourer who was sent to make a certain measurement and came back with the result as three bricks and half a brick and a hand and two fingers, furnishes an example. His measurement could be reproduced by himself — but it was useless to others. The length of a foot is quite a detail : it is only important that we should agree to call a particular length one foot. And the same appHes to temperature measurement; it is unimportant what a degree of temperature is, but we must all understand it and agree to it and be able to reproduce it.

The Fixed Points of Temperature. In making a scale of temperature it will be necessary to have two fixed points of temperature to which reference can be made at any time. One of these — the lower fixed point — is the temperature at which pure ice melts or pure water freezes. This is found to be a constant temperature. The other fixed point — the upper fixed point — is the temperature of steam over water which is boiling at standard atmospheric pressure. This is

64 HeM and Temperature [CH.

a rather complicated fixed point, and the reasons for its complexity lie in the following facts. Firstly the temperature at which water boils is largely affected by the presence of any impurities — such as dirt or salt — whilst the temperature of the steam above the water is not affected in any way by these. If we throw a few pinches of salt into a saucepan of boiling water we shall find that the temperature of the water will rise, but the temperature of the steam will remain as it was.

Secondly the temperature at which water boils is slightly affected by the kind of vessel it is boiled in. Water boils at a slightly higher temperature in glass than in copper, but the steam temperature is the same in both. These two points account for the choice of steam.

Thirdlj^ the temperature of steam depends upon the pressure to which it is subjected — rising with an increase of pressure and falling with a decrease. Daily changes of atmospheric pressure will affect the tem- perature of steam ; therefore in defining a fixed point of temperature we must clearly specify that the steam shall be under some definite pressure. Standard atmospheric pressure is defined as the pressure equiva- lent to 30 inches of mercury at sea level in latitude 45° at the temperature of the lower fixed point.

These fixed points are called the freezing 'point and the boiling point respectively.

Construction of Thermometer. The usual ther- mometer consists of a glass bulb and stem containing mercury or quicksilver. The flask shewn in Fig. 20 is not quite suitable for temperature measurements. It is too big : it will absorb a large quantity of heat itself : and it will need quite a long time to take up the temperature

V]

Heat and Tem2)erature

65

required. But the idea is sound enough and so we make a small bulb at the end of a tube of thick wall and very fine bore. That is to say we reduce the whole thing in proportion so that we get a reasonably small instrument which will- absorb very little heat. Then we use mercury instead of water because it conducts heat better ; it requires less heat to raise the tempera- ture of the same volume a given amount; it remains liquid over a wider range of temperature ; and it does not wet the glass, and therefore runs up and down the tube with greater ease.

Fig. 22

Fior. 23

We need not discuss the details of filling, sealing and resting of the thermometer. We need hardly say any- thing about the marking of the fixed points except to state that the thermometer bulb and stem as far as possible should be immersed in steam or in melting ice under the conditions specified in our statements of the

P.Y. 5

66 Heat and Temperature [CH.

fixed points of temperature. There is no doubt that every reader will be testing the fixed points of a thermometer in the laboratory and he can there study the arrangements which will ic^scinble those shewn in Figs. 22 and 23.

Scales of Temperature. It is rather unfortunate that there are three scales of temperature in existence and use. These three are known as the Centigrade, the Fahrenheit and the Reaumur respectively. Fig. 24 illustrates the essential features of these scales and their differences. Celsius, who gave us the Centigrade scale, called the freezing point 0 — written 0° C. — and the boihng point 100, and he divided up the interval into 100 equal parts each of which he called 1° C.

Fahrenheit originally took different fixed points : he took a mixture of ice and salt and he imagined that that was the lowest temperature which could be ob- tained and so called it 0° F. Then he took the tempera- ture of the human body as his upper fixed point and called it 100° F. The interval he divided up into 100 equal parts so that his scale was a Centigrade scale, though different from Celsius' scale. On Fahrenheit's scale the temperature of pure melting ice was found to be 32° F., and the boiling point 212° F. Thus the interval between the freezing and boihng points is 180 Fahrenheit degrees.

Reaumur's scale differs from Celsius' in that the boiling point is called 80° — because 80 is an easier number to subdivide than 100 !

Conversion from one scale to another. In this country both the Fahrenheit and Centigrade scales are used. The scale in common use is the Fahrenheit, the Centigrade being used for scientific work and by

V]

H^at mid Temperature

Q7

electrical engineers. Mechanical engineers have gener- ally used the Fahrenheit but there are signs of the more general adoption of the Centigrade scale. Conversion from one scale to another is a simple matter and should not be beyond the powers of our readers without any further assistance in these pages.

Upper Fixed Point

Lower Fixed Point

Fig. 24

It need only be pointed out that since 100 Centigrade degrees cover the same temperature interval as 180 Fahrenheit degrees and 80 Reaumur degrees therefore 1 Centigrade degree = ^ Fahrenheit degree = | Reaumur degree.

It must also be noted that since the scales start from different points the Fahrenheit temperature has a sort of handicap allowance of 32 above the other two. This

5—2

68 Heat and Tem))€ratkre [CH.

allowanoe must be added or subtracted according to the direction of conversion.

Thus 15°C. = 15C. degrees above the freezing point,

and since 1 C. degree = f F. degree,

.'. 15 C. degrees = 16 x § = 27 F. degrees,

i.e. 27 F. degrees above the freezing point,

.-. 15° C. = 27 + 32 = 59° F.

Similarly 15° C. = 15 x f = 12° Reaumur.

Again let us convert 113° F. to Centigrade and Reaumur.

113° F. = 113-32 F. degrees above the freezing- point = 81 F. degrees,

since 1 F. degree = f C. degree.

.•. 81 F. degrees above the f.p. = --g— C. degrees above f.p. = 45° C.

and 81 F. degrees above the f.p. = ~^ R. degrees above the f.p. = 36° R.

All readings below 0° on any scale are called minus quantities.

Other thermometers. The mercury-in -glass ther- mometer has a wide range of general usefulness but when temperatures below — 40° C. (which, by the way, is also — 40° F. as the reader should verify) are to be measured, some other form must be employed since mercury freezes at — 40° C. or F. Grenerally alcohol is used instead of mercury and it can be used down to — 1 10° C. For lower temperatures than this gaseous and electrical thermometers are generally used. These will be discussed later.

v] Heat and Temperature 69

For temperatures above 250° C. or 482° F. mercury thermometers must also be superseded. The boihng point of mercury is 350° C, but unless the upper part of the stem is filled with some inert gas it cannot be used beyond 250° C.

For higher temperatures recourse is usually made to a class of instruments called pyrometers. Some of these depend upon the expansion of solids, but the majority in use in engineering practice at the present time are electrical and depend upon the fact that when a junction of two dissimilar metals is heated a current of electricity is generated which increases as the temper- ature of the junction increases. This current operates a delicate detector — really a voltmeter— the scale of which is marked off directly in degrees of temperature. These are very valuable instruments and are of great service in measuring any high temperatures such as superheated steam, flue temperatures, boiler-plate temperatures and so on. Fig. 25 is a diagram illus- trating the principle of a pyrometer as supplied by

Fig. 25

Messrs R. W. Paul. We cannot well discuss it in detail since it is possible that many readers have not progressed sufficiently into the study of the sister science of electricity to be able to appreciate

70 Heat and Temperature [CH.

it. Those who have will be able to understand it well enough from what has been said.

Self-registering Thermometers. If it is desired to know the highest or lowest temperature reached during any particular interval of time a self-registering ther- mometer is used. A simple form (Rutherford's) of maximum thermometer is shewn in Fig. 26 (a), and (6) illustrates the thermometer for recording the minimum temperature. The maximum thermometer is just an

I

D

(a)

Yi.i.^^yyyy^^yyyy.-r^':^:^,

(b) Pig. 26

ordinary mercury thermometer provided with a little index I which can slide freely along the tube. As the mercury expands it pushes the index along and when it contracts the index will be left /'. The position of the left-hand end of the index will be the maximum temperature recorded since the index was last set in position against the thread of mercury.

The minimum thermometer contains alcohol instead of mercury and the index is placed inside the alcohol in the tube. As the alcohol contracts this index will be drawn back, but when the temperature rises again it will remain at its lowest point. Of course the index must be small enough not to impede the flow of alcohol up the stem. The indexes are set in position by tilting the thermometer and tapping them gently. In some forms they are made of iron and are set in position by means of a small magnet.

v] Heat and Temperahn'e 71

Fig. 27 illustrates the doctor's or clinical thermo- meter. The bore of the tube is constricted at the point a. When the mercury is expanding the force of expansion is great enough to push the mercury through this narrow part of the tube ; but on con- tracting the thread of mercury breaks at the con-

i""i'"'r"'i-F'i|""i"ii|""i""i""i""M"'i""i

r)

Fig. 27

striction thus leaving the thread in the stem at the same position it occupied when in the patient's mouth. Before the thermometer can be used again the thread must be shaken down — an operation frequently re- sulting in disaster to the thermometer.

EXAMPLES

1 . Convert the following Centigrade temperatures to Fahrenheit : 36°, 2000°, - 273°, - 40°.

2. Convert the following Fahrenheit temperatures to Centigrade : 10°, 0°, - 40°, - 400°, 98-4°, 2000°.

3. Convert the followmg Reaumur temperatures to Fahrenheit and to Centigrade: 12°, - 32°, - 218-4°, 160°.

CHAPTER VI

EXPANSION OF SOLIDS

One of the chief effects of heat upon matter is the change of volume which it produces. In the vast majority of cases an increase in the temperature of a body is accompanied by an increase in the volume, but there are cases in which the converse is true.

In the case of sohds we may have expansion of length, breadth and thickness — and this is generally the case. India-j-ubber in a state of tension contracts in length when heated — but its volume increases. All metals however expand proportionately in all direc- tions. If a sphere of metal be heated it will expand but will still be a sphere. All metals expand with increase in temperature and contra<)t with decrease in temperature, and metals expand more than any other solids under the same conditions. Further, different metals expand differently under equal conditions.

Laws of expansion. We will consider firstly the expansion of length or Hnear expansion of a substance. It has been shewn — and can be shewn again by the apparatus illustrated in Fig. 28 — that the length of a solid increases uniformly with the increase in tempera- ture. An increase of 20° of temperature will produce twenty times the increase in length which would be produced by a 1° increase in temperature.

CH. vi] Expansion of Solids 73

Secondly it can be shewn in the same way that the actual amount of expansion produced for a given in- crease in temperature depends upon the original length of the substance. That is to say a 10 foot length of metal would have a total expansion 10 times greater than a 1 foot length of the same metal for the same increase in temperature.

Thirdly, the expansion produced depends upon the substance which is expanding. Obviously if we wish to compare the expansion of different substances we must take equal lengths and heat them through equal ranges of temperature. It is also obvious that it would be most convenient to take unit lengths and to heat them through 1° of temperature.

Coefl&cient of linear expansion. The increase in the length of a unit length produced by increasing the temperature 1° is called the coefficient of linear expansion of a substance.

Strictly, the definition given above is not true. It should be the increase in the length of a unit length at the freezing point when increased 1°. But the value of the coefficient is so small that for all practical purposes the definition with which we started is sufficiently accurate and is certainly simpler.

A foot of brass when heated 1° C. becomes 1-0000188 foot. Similarly 1 centimetre . of brass when heated 1° C. becomes 1-0000188 centimetre. From our defini- tion it follows that the coefficient of linear expansion of brass is 0-0000188 per degree Centigrade, and we can readily see that if an increase of 1° C. produces an increase in length of 0-0000188 unit, then an increase of 1° F., which is only {}th of a degree Centigrade, will only produce an increase in length of {} x 0-0000188 or

74 Expansion of Solids [ch.

0-00001044 unit. That is to say the coefficient of expansion per degree Fahrenheit will only be fjths of that per degree Centigrade.

Again though we have only spoken of exjjansion, the same laws exactly apply to contraction produced by a decrease in temperature, and we might even define the coefficient of expansion (or contraction) as the increase (or decrease) in the length of a unit length of a substance for an increase (or decrease) of 1° of tem- perature.

Calculations. Calculations are obviously quite simple for we have only to remember that the increase (or decrease) in length is directly proportional to

(tt) the increase (or decrease) in temperature,

(b) the original length,

(c) the coefficient of linear expansion of the sub-

stance, and we can apply the simple rules of proportion. There is clearly no need to deduce any formula for such straightforward work.

Example. A rod of copper is 33" long at 15° C. : what will be its length at 100° C, the coefficient of linear expansion of copper being 0-0000172 per degree C.

It follows therefore that

1 inch of copper heated through 1° C. expands by 0-0000172 of an inch, .

.'. 33 inches of copper heated through 1° C. will expand by 33 x -0000172",

.*. 33 inches of copper heated through 85° (i.e. 100-15) will expand by 33 x 85 x -0000172" - 0-048246".

Therefore the length of the rod at 100° C. will be 33-048246" or, as we should express it in practice, 33-048".

VI]

Expansion of Solids

75

Determination of coefficient of linear expansion.

Fig. 28 illustrates a simple form of apparatus which can be used to determine the coefficient of expansion of a solid. The rod R to be tested is placed inside a jacket J which can be filled with steam or water at any desired temperature. The rod is fixed between two screws as shewn, AS being an adjusting screw and MS a micrometer screw. The micrometer is adjusted to zero and the rod is tightened up by means of the adjusting screw. This should be done at the higher temperature first. Then the temperature of J is lowered and the micrometer screw is turned until the

Fig. 28

rod is tight again. The decrease in the length of the rod is thus given by the micrometer screw : the original and final temperatures are given by the thermometer : and the original length of the bar is obtained by re- moving the rod and measuring it with a straight-edge. From these particulars the coefficient of linear expan- sion may be calculated.

The above method is not very accurate, the chief source of error lying in the expansion and contraction of the screws. But it will serve to illustrate the general principle and the reader will be quite able to understand

7(5

Eaypaiision of Solids

[CH.

the many more refined arrangements for this measure- ment if he understands this one.

Table shewing some coefficients of linear expansion per (legrec Ceriliijrade.

Zinc

Copper ... Iron, sof t . . . Steel, soft

Nickel steel (^li^o nickel Nickel steel (45 % nickt Cast iron Tin Lead Silver Gold

Platinum . Porcelain . Glass (soft) These numbers represent

... 000(X)294

0-()000172

0(XX)0122

0-0(XX)108

) ... 0-00000087

1) ... 0-0tKX)082

... 0-0(X)011

... 0-000025

... 0-000028

... 0-000021

... 0-000015

... 0-000009

... 0-0000088

... 0-000009

average values only.

Some advantages of expansion and contraction. Much practical advantage can be taken of the expansion and contraction of substances due to temperature changes. The forces exerted by the expansion or contraction may be very great and they are used to advantage in such operations as fixing iron tyres on wheels and other "shrinking" operations. The tyre is made of such a size that it will just fit on to the wheel when it is hot and the wheel is cold. When the tyre cools it grips the wheel tightly. Similarly one sleeve or cylinder may be shrunk on to a smaller cylinder.

Then we have a very universal application in the case of hot ri vetting. The plates are drawn tightly together by the rivetters with their hammers— but the

vi] Expansion of Solids 77

contraction of the rivet as it cools will always exert an additional force.

The forces exerted by expansion and contraction of an iron bar may be shewn very strikingly by means of the apparatus sketched in plan in Fig. 29. JS is an iron bar having a screw thread and a large nut S at one end and a hole through which a cast iron pin P is inserted at the other end. The screw can be adjusted so that the bar is held rigidly between the end fixtures on the metal base. If the bar is heated the pin P will be broken or the bar B will buckle. The force of contraction can also be shewn by placing the pin and the nut on the other sides of the end fixtures and tightening up whilst the bar is hot. On cooling the pin will be broken.

Fig, 29

Small automatic switches for switching an electric lamp on and off at frequent intervals are amongst other applications of the expansion of metals.

If two equal lengths of different metals be rivetted together closely then when this compound bar is heated it will bend so that the metal which expands the greater amount will be on the outside of the curve. On cooHng it will bend in the opposite direction. Fire alarms which operate an electric bell are often made on this principle, and the balance wheel of a watch is compen- sated in the same way.

78 Ea^pcmmcm of Sollth [ch.

Some disadvantages of expansion and contraction. Nobody suffers more from the drawbacks of expansion than the engineer. Fortunately the effects can always be compensated — but such compensation has to be nicely adjusted and necessarily adds to the cost. Every- one knows why railway lines are laid in sections, why no two rails butt on to one another, why the rails are "fixed" in chairs with wooden wedges, and why they are "fixed" together with fish plates. And a" httle calculation will shew why the lengths of the rail sections in use are not greater than they are. It would be bad for rolling stock, rails and passengers if we had to leave large gaps between sections : and even as it is there is a distinct difference between summer and winter travelling.

Tramway rails are buried— and thus we have not the same trouble because the rail temperature will never differ appreciably from the earth temperature. But of course it is too costly a method for long distance railways.

Every branch of structural engineering has to take this expansion and contraction into consideration. The Forth Bridge is built in such a way that a total change of length of 18 inches must be allowed for between winter and summer. Clearly, it must not be taken up all at one place.

Furnace bars must fit loosely : pipe joints of exposed gas or water mains must be telescopic : patterns for castings must be Qf such a size that they take account of the contraction of the metal, and sometimes must be designed specially to prevent fractures which may be produced by one part of the casting coohng quicker than another part and setting up undesirable stresses.

VI]

Expansion of Solids

79

I

The standard yard measure is only correct kt one temperature, 60° F.

A clock regulated by a pendulum will gain or lose as its pendulum contracts or expands. There are many devices for compensating pendulums all of which depend upon the fact that different substances expand differently. The gridiron pendulum affords us a useful example since this principle is also applied to other compensations. Fig. 30 illustrates this. Two different metals are used, iron and zinc. The iron rods can expand downwards and the zinc rods can expand upwards. The lengths of / and Z are chosen so that the total expansion of the iron is the same as that of the zinc. In this way the position of the centre of gravity of the pendulum bob will re- main constant.

Surface or superficial expansion. If we take a square of a metal of side 1 foot and heat it, it will expand in all directions. If we heat it 1° and if its coefficient of expansion is K then each side will he, {\ + K) feet. Therefore its area wiU become (1 + KY square feet, Fig. 30

that is 1 + 2K + K^ square feet. That is to say the coefficient of superficial expansion is {2K + K'^). Now since K is always a very small quantity it follows that K^ will be much smaller and indeed is so small that it can be neglected in comparison with 2K. It is therefore usual to say that the coefficient of superficial

}{0 E.vpansicni of Sol'uh [CH. vi

expansion is twice that of linear expai}f<ion and of course is expressed in square meoMire.

Cubical or voluminal expansion. In the same way if we take a cube of 1 foot side and heat it 1° of tempera- ture each side will become I + K feet and its volume will become {I + Kf cubic feet or I + 3K + 3K^ + K^ cubic feet. The coefficient of cubical expansion is thus {3K + 3Z2 + K^) but again we may neglect {3K^ + K^) in comparison with 3K, and it is usual to say that the coefficient of cubical expansion is three times that of linear expansion expressed in cubic measure.

EXAMPLES

1. What is the expansion of an iron rail 37 feet long at 00° F. when it is heated to 140° F. ? The coefficient of expansion of the rail = 0-000012 per degree Centigrade.

2. The distance from London to Newcastle is 27 1 miles. What is the total expansion of the rails between the lowest winter tempera- ture (say 10° F.) and the highest summer temperature (say 120° F.) ?

3. What must be the length of a rod of zinc which will expand the same amount as 39-2 inches of iron? See table on p. 76 for coefficients of expansion.

4. A plate of copper is 10" x 8" at 15° C. What will be its area at 250° C. ?

5. A sphere of brass has a diameter of 2-2"' at 32° F. What will be its volume and what its diameter at 212° F. ?

6. The height of a barometer at 15° C. is found to be tO cms. when measured with a brass scale which is correct at 0° C. What is the true height of the barometer ?

7. A certain rod is 36 inches long ai 0° C. and 30-04 inches at 50° C. What is the coefficient of expansion of the rod ?

CHAPTER VII

EXPANSION OF LIQUIDS

Obviously we are only concerned with change of volume in the case of liquids, since they have no rigidity. Further they must be in some kind of a containing vessel and since in all probability this will expand we shall have to be careful to distinguish between the real and the apparent expansion of the liquid. The experiment illustrated by Fig. 20 indicates this. If we know the increase in the volume of the containing vessel and the apparent increase in the volume of the liquid the real expansion of the liquid will be the sum of the two.

The coefficient of real expansion will therefore be greater than the coefficient of apparent expansion by an amount equal to the coefficient of expansion of the material of the containing vessel.

Most liquids— molten metals excepted — do not ex- pand uniformly. Fig. 31 is a graph illustrating the relationship between the volume and the temperature of a given mass of water. It is seen that the change in volume per degree of temperature is an increasing quantity after a temperature of 4° C. has been passed. It is therefore clear that we cannot give a number which represents the coefficient of expansion of water. We can give it for a definite range of temperature, but that

P.Y. 6

82

ExpansiitH <>/ Liquids

[CH.

is all. Thus between the temperatures of 4° C. and 14° C. the mean coefficient of expansion (real) of water is 0-00007. but between the temperatures of 50° C. and 60° C. it is 0-00049.

1-0020 1-0010

1-000

/

^^

^

/

(

fC 4° {

>" 1

0° 1

5° 20°

Temperature Fig. 81. Volume and Temperature of Water

Methods of determination of coefficient of expansion.

The apparent coefficient, in glass, may be obtained readily by means of a glass bulb (of known volume) having a stem graduated in terms of the bulb's volume. This is filled to a certain point up the stem. It can then be immersed in a bath the temperature of which can be adjusted to any desired value, and the apparent volume at each temperature can be read off.

The real or absolute expansion is usually determined by comparing the density of the liquid at one known temperature with its density at 0° C. or at any other known temperature. As density is the mass of a unit volume it follows that as the volume of a given mass

I

VIl]

Expansion of Liquids

83

increases, its density decreases. Fig. 32 illustrates a form of apparatus by means of which this measurement may be made. The hquid to be tested is placed in the large U-tube, each limb of which is surrounded by a

/

Steam inlet

Steam outlet

-^

-^~

& Water I outlet

Cold water

Fig. 32

jacket through which we can run cold water or steam or water at any desired temperature. The U-tube is open to the atmosphere and if both limbs are at the same temperature the liquid will be at the same level in each. If we pass ice cold water through one jacket

6—2

84 E.rjMUision of LiqultLs [oh.

and steam through the other then the density of Hcjuid in the hot hmb will be less than that in the cold limb and therefore we shall get a difference in level since a longer column of hot liquid will be needed to balance a given column of cold liquid. We then measure the heights of the columns H and h and note the tempera- ture of the two jackets.

The heights H and h are inversely proportional to the densities which we may call Dq and D^ .

The densities are inversely proportional to the volumes.

Therefore the heights are directly proportional to the volumes.

That is to say H : h = volume at the higher tem- perature : volume at the lower temperature.

Therefore the coefficient of expansion between the temperatures chosen

, H-h

A (difference in temperature) '

There have been several elaborations of this prin- ciple of measurement notably by Regnault and Callendar : but the fundamental principle is the same and the elaborations aim at producing greater accuracy.

Peculiar behaviour of water. If we look at Fig. 31 again we notice that as the temperature of water is increased from 0° C. the volume of the water decreases and becomes a minimum at 4° C. after which it increases again. Water is unique in this respect and the tempera- ture at which th6 water has its least volume is known as the temperature of maximum density, namely 4° C. or 39-2° F. The unit of mass on the metric system is one gramme, which is the mass of a cubic centimetre of water at 4° C.

%

vii] Expansion of Liquids 85

The immediate effect of this pecuUar behaviour of water is the preservation of animal and vegetable life in lakes and ponds in winter time. The water below the ice will never fall below this temperature of 4° C, or 39-2° F. because at any other temperature higher or lower it will be Ughter bulk for bulk and will therefore remain on top. As a pond cools down (it should be noted that this cooling will only take place at the surface) the water at the top will contract and sink until the whole pond is at 4° C. On further cooling the surface water will become lighter and will remain on the top and so will ultimately freeze. But the water below the ice will be at 4° C. Water and ice are bad conductors of heat and thus the pond will never become frozen to any great depth. It is well known that an ice coating on a pond should be flooded each night if it is desired to get thick ice on the pond.

The table given below shews how the density and the volume of water changes between the temperatures of 0° C. and 8° C.

Temperature

Density

Relative volume

0°C.

0-99987

100013

2°C.

0-99997

1-00003

4°C.

1-00000

1-00000

6°C.

0-99997

1-00003

8°C.

0-99989

1-00012

CHAPTER VIII

EXPANSION OF GASES

As we saw in Chapter III the volume of a gas depends upon the pressure to which it is subjected. It therefore follows that in considering how volume changes with temperature we shall have to be careful to keep the pressure of the gas constant,

Charles found that gases expand uniformly and that as far as he could ascertain all gases have the same coefficient of expansion, namely 0-00366. As a matter of fact later experimenters have found that this is not strictly true, but it is sufficiently near the truth for our purpose.

Gases expand much more than do soHds or Uquids under equal conditions and we have therefore to be more careful and particular about our definition of the coefficient of expansion. We must remember that the coefficient of expansion of volume of a gas is the increase in volume of a unit volume at 0° C. when heated from 0° to 1° C.

We had better look at the importance of this. Let us suppose for exa6iple that that coefiicient of expansion was ^th. Now a volume of 1 at 0° C. would become M at 1° C, and 1-2 at 2° C. and so on. But if we take the volume of 1-1 at 1° C. and to find its volume at 2° C. we were to take jj^ ol 1-1, viz. 0-11, and add this

CH. viii] Expmisimi of Gases 87

on to the original volume we should get a volume of 1-21 at 2° C.

This does not agree with the result we get by working from 0° C. So that if we are given that a certain gas has a volume of 1-1 at 1° C. and we are asked to find its volume at 2° C. we must first find what its volume would be at 0° C. and calculate from that point.

In cases where the coefficient is small we need not bother to find the volume at 0° C. since the error caused would be quite negligible for practical purposes. We have adopted this view already in our examples on the expansion of solids, but in the case of a gas it will be necessary to work from the temperature of 0° C

Charles' Law. Charles' law states that if a given mass of a gas be kept at a constant pressure and heated, the increase in the volume will be directly proportional to the increase in the temperature.

If we represent the volume of a given mass of gas at constant pressure by Vq at 0° C. and by Fj at some temperature t° C. then according to our definition the coefficient of expansion K will be given by

Fo(«-0) FoX^ ' i.e. the change in volume per unit volume at 0° per degree C.

/. F,-Fo=FoxZx«,

.-. F, = (Fo X Z X 0 + Fo, or Vt == Fo (1 + Kt).

Therefore we can easily find the volume at 0° C. and from that we can find the volume at any other desired temperature.

Example. A given mass of a certain gas is 12 c.c.

iW Expansion of Gaaes [ch.

at a temperature of 15° C. ; what will it be at 60° C, the coefficient of expansion being 0-00366 ? Firstly we find the volume at 0° C. ^15= ^o(l + -00366 X 15), 12 = Fo(l + 15 X -00366),

Then we find the volume at 60° C. from ^60= ^o(l + -00366 X 60), .-. F6o= 11-375 X 1-2196 = 13-875 c.c.

Experimental verification. Charles' law may be verified and the coefficient of expansion of a gas determined by the dilatometer method similar to that described in the previous chapter.

A bulb of known volume having a graduated stem can be arranged as shewn in Fig. 33. The bulb and

Fig. 33

part of the stem can contain air or any other gas and this is shut off from the outside air by means of a small pellet of mercury P which also serves as an index. If the volume of the bulb is fairly large compared with the stem the errors due to the exposed part of the stem will be very small, but the range of temperature which can be covered will not be very great. This should be

viii] Expansion, of Gases 89

determined by a preliminary experiment. Then the bath is heated up to the highest permissible temperature and readings are taken, as the bath cools, of tempera- tures and volumes. These can be plotted graphically and coefficients can be calculated from the various readings. The volume at 0° C. can be determined by experiment or can be obtained from the graph.

Any bulb and stem may be readily calibrated by filling with mercury, and then weighing the mercury required. Similarly the volume per inch of tube can be determined by measuring the length of any pellet of mercury in the tube and then weighing it. From the density of the mercury and its mass the volume is calculated since density is the mass of a unit volume.

There are again many more refined and elaborate devices for the verification of Charles' law, but if the principle of this is understood, the refinements can be appreciated quite readily by the intelligent student.

Variation of Pressure with Temperature. We all know that if we confine a gas to a given space and heat it the pressure of that gas increases. Such pressure plays the all-important part in internal combustion engines and in the use of explosives. We have all witnessed the disasters to our air balloons in bygone days when they got too near to the fire.

Regnault shewed that if the volume of a given mass of a gas was kept constant and its temperature increased the increase in the pressure was directly proportional to the increase in temperature.

He found moreover that the coefficient of increase of pressure — namely the increase in the pressure of a unit pressure at 0° C. when heated 1° C. — was the same as the coefficient of increase in volume, -00366 or ^j.^.

90

Exj/ansiou of (jiittfs

L<;ii.

Fig. 34

A simple form of apparatus for the verification of this law is shewn in Fig. 34. A hulb which contains the gas O is immersed in a bath B the temperature of which can be varied at will and determined by the ther- mometer T. The bulb is con- nected by a fine bore tube to one of the limbs of a U -tube — similar to the apparatus used for the verification of Boyle's law (page 43). By raising or lowering the right-hand limb R the mercury in the left-hand limb can be kept at the same position for various tempera- tures of the bath. The actual pressure of the gas at each temperature will be the atmospheric pressure in inches or centimetres of mercury plus or minus the difference in the levels of the mercury in L and R in inches or in centimetres — the volume of the gas being kept constant at each temperature by the adjustment of JR.

Absolute zero of temperature. If, instead of using a mercury thermometer for the measurement of tem- perature, we use a gas thermometer — either on the constant volume or on the constant pressure principle — we should find a theoretical minimum temperature below which we^ could not use it. That is to say if we assume for a moment that the law of Charles and the corresponding pressure-temperature law hold good for all temperatures we should find that at a temperature of — 273° C. gases would have no volume and would

viii] Expansion of Gases 91

exert no pressure. This temperature is called the absolute zero of the perfect gas thermometer.

Now it is not considered possible to annihilate matter at all, so that we must feel that there is a way out of this mystery. It lies in the fact that gases change into liquids before they reach that temperature and after that they no longer follow Charles' law.

According to the Kinetic Theory of Gases (page 8) the pressure of a gas is caused by the agitation or bom- bardment of its molecules. Therefore if the gas exerted no pressure its molecules must be stationary. It is further suggested that as a body contains more and more heat the movement of its molecules is increased and vice versa. Therefore if we can reduce a gas to such a temperature that it exerts no pressure there will be no molecular movement and no heat. That temperature would therefore be the lowest possible or the absolute zero of temperature.

The temperature of — 273° C. has never been reached in practice although in recent times the temperature of — 269° C. has been obtained.

Fig. 35 shews a volume -temperature graph, volumes being plotted vertically and temperatures horizontally. If we get readings of the volume of any mass of a gas between 0° C. and 100° C. and then produce the graph backwards (assuming Charles' law to hold good) until the volume is zero we find that the temperature for this condition is - 273° C.

It will be quite clear to our readers that if this point, — 273° C, were made the origin of the graph, that is to say if it were both a zero of temperature and volume, we could say that the volume was directly proportional to the temperature calculated from this zero.

92

ExpanMOit of Gaiio

[CH.

From tills we have adopted another temperature scale — called the Absolute scale — having the tempera- ture of — 273° C. as its zero and being equal to the Centigrade scale reading + 273. Thus 0° C. = 273° A.,

57° C. = 57 + 273 = 330° A.,

and - 38° C. = - 38 + 273 = 235° A.,

and so on. Charles' law may now be stated thus:

©"A 73'A

-IOO°C

I

I I I73''A

IOO°C 200°C

Temperature \

I I I

273°A 373°A 473°A

Fig. 35

that the volume of a given mass of a gas kept at a constant pressure varies directly with the absolute temperature.

Thus if PJi be the volume at Tj° Absolute, and Fg be the volume at ^2° Absolute, then

Fi ^ Tj _ tj° C. + 273 Fa" T2"^2°C. + 273' In the same way it can be seen that if the volume

viii] Expansion of Gases 93

is kept constant the pressure will vary directly as the absolute temperature :

P, ^ TIA.

P2 ^2°A.- Finally if we consider possible variations of each of the three quantities pressure, volume and absolute tem- perature, we shall find that

when Pj, Fj and T^ are the pressure, volume and

absolute temperature in one case, and Pg, V2 and T^

those in the second case.

Examples. (1) Let us take the example on page 88.

A given mass of a gas is 12 c.c. at 15° C. ; what will

it be at 60° C. ?

Vi Ti . 12 _ 15+273 _ 288 Fa ~ ^2 ' • • F2 " 60 + 273 ~ 333 '

••• ^2= ^-^jgl^- 13-875 c.c.

We see that it is much easier to solve the problem this way.

(2) A mass of air has a volume of 24 c.c. at a temperature of 27° C. and a pressure of 30" of mercury. What will'be its volume at 77° C. and a pressure of 20" mercury?

•^2^2 ^ 2

24 X 30 300

• • F2 X 20 350 ' „ 24x30x350 ,„ •• ^^ = -20-^3-00 ^1^^-

Absolute-Fahrenheit scale of temperature. Before

94 Expamion of Gases [CH. viii

concluding this chapter it may be well to point out that the absolute zero of temperature on the Fahrenheit scale would be — 459- 2°. By adding 459-2 to any Fahrenheit reading we shall get an Absolute-Fahrenheit scale. This scale could be used for the above calcula- tions.

For example : If a certain gas has a volume of 12c.c. at 59° F., what will be its volume at 140° F.? Fi _ Ti°A. F2 T2°A.' and using the Absolute-Fahrenheit scale T^ is

459-2 + 59 = 518-2° and Tg is 459-2 + 140 = 599-2°,

12 518-2 • • F2 ~ 599-2 ' . „ 12 X 599-2 ,^„^^

EXAIklPLES

1. A certain mass of air has a volume of 50 cubic inches at 16° C, what will be its volume at 0° C. and at IW V.. the pressure being constant ?

2. A certain mass of air has a volume of 3 cubic feet when the temperature is 27° C. and the pre-ssure is 15 lbs. per square inch: what will be its volume when the temperature is 227° C. and the pressure is 150 lbs. per square inch ?

3. A certain mass of a gas at a temperature of 59-8° F. has a volume of 36 cubic feet, the pressure being 20 lbs. per square inch. If the temperature be increased to 212° F. what must be the pressure in order to keep the volume the same ?

4. The volume of a certain mass of gas is 8 cubic feet at 15 lbs, pressure and temperature 20° C. If the pressure be doubled find the temperature to which it must be heated so that its volume becomes 6 cubic feet.

CHAPTER IX

MEASUREMENT OF HEAT

One of the effects which heat may produce when given to matter is an increase in temperature. This effect is not inevitable, but generally speaking a body becomes hotter when it receives heat. An exception may be quoted at once. If we put a vessel of water over a furnace we shall find that the water will get hotter and hotter (as shewn by a thermometer placed in it) until it starts to boil. But we shall find that it does not get any hotter after that. We may increase the temperature of the furnace as much as we please but the thermometer will not rise beyond the boiling point. Of course the water will boil away more quickly, and the heat is being used to produce this change of the state of the liquid.

However, whenever heat is given to a substance which is neither at its boiling point nor melting point an increase in temperature will follow. It is readily conceivable that if two equal quantities of a substance are given equal quantities of heat they will be equally affected so far as temperature increase is concerned. It is also conceivable that if a certain quantity of heat be given to a substance and it produces a certain in- crease in its temperature, twice the quantity of heat will produce twice the increase in temperature. For

96 Measurement of Heat [ch.

all practical purposes this is true (just as a pint of liquid will rise to twice as great a level in a cylindrical vessel as half a pint) but actually it is not strictly the case. We shall, however, assume that it is, since the very small error involved is of little or no account in engineering practice.

Unit of Heat. A unit quantity of heat energy is defined as that quantity necessary to raise the tempera- ture of a unit mass of water through one degree of temperature.

Thus on the British system of measurement a unit of heat is the heat necessary to raise the temperature of 1 lb. of water through 1° F. This is called a British Thermal Unit and is commonly used by mechanical engineers.

The quantity of heat necessary to raise the tem- perature of 1 gramme of water through 1° C. is the unit of heat on the metric system of measurement. This is called a Calorie.

These units are not equal of course : and since there are 453-6 grammes to the pound and ^ of a degree Centigrade to the degree Fahrenheit it follows that there are 252 calories to the British thermal unit.

It will be noted that water is chosen ^s the standard substance. We shall see presently that different sub- stances require different quantities of heat per lb. to produce one degree rise in temperature.

Every unit mass of water will require a unit of heat for every degree its temperature is raised : and con- versely, on cooling, every unit mass will give out a unit of heat per degree fall in temperature. Thus the heat necessary to raise the temperature of 3 lbs. of water from 60° F. to 212° F. will be 3 x (212 - 60), viz.

ix] Measu7'ement of Heat 97

3 X 152 or 456 b.th.u. The heat given out by 4-5 lbs. of water cooHng from 60° F. to 32° F. will be 4-5 X (60 — 32), viz. 126 b.th.u. That is to say the heat required or yielded by any mass of water M when it undergoes a change of temperature from t-^ to t^ will be

M X (^2° - ^1°) units.

The units will be calories if M is in grammes and t^ and ^2 s-re Centigrade ; and they will be British thermal units if M is in lbs. and ^^ and t^ are Fahrenheit.

Specific Heat. If we take equal masses of iron and copper and heat them to the same temperature and then plunge them into two equal vessels of water at the same temperature, we shall find that the vessel into which we plunged the iron will become a little hotter than the other one. This suggests that the iron must have given out more heat than the copper. The heat given out must have been received by the water : and its temperature would rise. In the same way if we take equal masses of other different substances at equal temperatures and plunge them into separate equal vessels of water we shall find that these different sub- stances give out different quantities of heat.

The quantity of heat necessary to raise the temperature of a unit mass of a substance through 1° is called the specific heat of that substance.

The specific heat of copper, for example, is 0-094. That is to say 0-094 British thermal unit of heat will raise the temperature of lib. of copper through 1° ^, It also means that 0-094 calorie of heat will raise the temperature of 1 gramme of copper through 1° C

9H

Meamtrement of Meat

CH.

The following table gives the specific heats of some substances :

«ilvfr (»or)r)

Copper ()()!»4

Iron 0112

Mercury ... . . ... ... OO'.i'.i

Glass ()•!!)

Turpentine ... ... ... ... 0-43

AluminiuTu ... ... ... ... 0-21

Lead 0031

Water • 1

Ice 0-502

Hydrogen (constant pressure) ... 3-402

Air (constant pressure) 0-2427

Air (constant volume) 0-171.5

The fact that water has such a high specific heat compared with most other things is not generally appreciated by the man in the street. He is always inclined to think that a kettle absorbs as much if not more heat than the water it contains, and may even advocate the use of thinner kettles. Let us consider how much heat will be absorbed by a kettle made of copper, weighing 2 lbs., and containing 3 lbs. of water when heated from 70° F. to 212° F.

Firstly, the kettle :

1 lb. of copper heated through 1° F. will require 0-094 unit of heat,

therefore 2 lbs. of copper heated through 1° F. will require 2 x 0-094 units of heat,

therefore 21bs. of copper heated through (212 — 70)°F. will require 142 x 2 x 0-094 units of heat.

That is to say the kettle will absorb 26-7 units.

ixj Measurement of Heat 99

Secondly, the water :

1 lb. of water heated through 1° F. will require 1 unit of heat,

therefore 3 lbs, of water heated through 1° F. will require 3 units of heat,

therefore 3 lbs. of water heated through (212 — 70)°F. will require 3 x 142 units of heat.

That is to say the water will absorb 426 units.

Thus we see that the total heat absorbed by the kettle and the water is 452-7 units of which only 26-7 units are taken by the kettle.

Water Equivalent. We could have taken it in a simpler way than this. Since 1 lb. of copper only absorbs 0-094 unit of heat for each degree rise in tem- perature, we can say that 1 lb. of copper is only equivalent to 0-094 lb. of water, since 0-094 lb. of water would absorb 0-094 unit for each degree increase. Therefore we could say that the kettle — viz. 2 lbs, of copper — was equivalent to 2 x -094, viz. 0-188 lb. of water, so far as the absorption of heat is concerned. We could then take it that the kettle and the water were together equivalent to 3-188 lbs, of water, and if 3-188 lbs, of water are heated from 70° F, to 212° F. the heat required will be 3-188 x (212 - 70), viz. 452-7 units, which agrees with the previous answer.

Thus we can say that the mass of any substance multiplied by its specific heat is the water equivalent of that substance. This is of some assistance to us in our experiments connected with the measurement of heat.

Measurement of Specific Heat. The substance whose specific heat is to be determined must be weighed, and it is heated in some way or other to some known or measurable temperature. It is then dropped into

7—2

100 Measurement of Heat [ch.

a vessel containing a known quantity of water at a known temperature. The "mixture" is thoroughly stirred and its temperature is taken. From these particu- lars the specific heat of the substance may be calculated.

It will be seen at once that there are certain practical difficulties connected with this experiment. Pre- cautions must be taken to avoid loss of heat as the substance is being dropped into the water ; and again, precautions niust be taken to prevent loss of heat from the water to the surrounding air.

The vessel containing this water is usually called a calorimeter and generally consists of a cyhndrical copper vessel which is suspended inside a similar but larger vessel by means of three silk threads. The surfaces are kept well polished and the calorimeter losses are thus reduced to a minimum. In addition to this it is usual in important measurements to arrange that the first temperature of the water in the calorimeter shall be as much below the temperature of the surrounding air as the second temperature is above. In this way we get a slight gain balancing off a slight loss.

The arrangement for heating the substance generally takes the form of a steam jacket J, J as shewn in Fig. 36. The substance S is suspended inside and a thermometer T is fixed near it. The heater is fixed on an insulating base with a sliding shutter which has the effect of opening or shutting the heater. The calorimeter is placed directly beneath the centre of the heater. When the jacket is heated and its temperature has been noted, the shutter is opened and the substance is lowered into the calorimeter as speedily as possible. The calori- meter and its contents are then removed, stirred, and the temperature read.

IX]

Measurement of Heat

101

Let us suppose that the following results were obtained.

Mass of calorimeter empty 45 grammes.

Material of calorimeter, copper of specific heat 0-094.

(N.B. Only the inside vessel should be weighed as the outer vessel does not absorb any heat.)

Mass of water in calorimeter 132 grammes.

Original temperature 15° C.

Shutter

Calorimeter

Fig. 36

Mass of substance in calorimeter 116 grammes. Original temperature of substance in heater 92° C. Final temperature of "mixture" 22° C. The water equivalent of the calorimeter

= 45 X 0-094 = 4-2 grammes.

102 Meamirement of Heat [CH.

Therefore the total equivalent mass of water

= 132 + 4-2 - 136-2 grammes. Therefore the heat received

= 136-2 X (22'- 15) = 953-4 units. Now this heat must have been given out by 116 grammes of substance cooling from 92° to 22°, that is, through 70°.

Therefore the heat which would be given out "by 1 gramme cooling through 1°

= ,?«--, = <>••''■

116 X 7

Therefore the specific heat of the substance = 0-117.

In all heat measurements our results are determined from the following fact :

Heat received by calorimeter and water = heat given by substance inserted.

There is no need for us to express any of this as mathematical formulae. The fundamental ideas are quite simple, and the examples can be and should be worked out from first principles.

Calorific value of fuels. It is often very important that engineers should know how much heat is given by burning a known quantity of different kinds of fuel. As we have said before we buy fuel for the heat energy which we can get out of it, and the cheapest fuel is that w^hich will give the greatest amount of heat for every shilling which we pay for it.

The number of heat units per unit of mass of fuel is called the calorific value of that fuel.

One of the methods of determining this value is by the use of the Darling calorimeter, the main ideas of which are illustrated by Fig. 37,

IX]

Measurement of Heat

103

A known mass of the fuel is placed in a small crucible C which is placed inside a bell jar B. This jar is fastened down to a special base plate. The products of combustion can only leave the jar through the outlet at the bottom of the base-plate, and this outlet R is like a watering-can rose with very fine holes. A supply of oxygen — which, of course, is necessary for the combustion of the fuel — is admitted at the top of

Oxygen inlet

Fia;. 37

the bell jar and its rate can be regulated by means of a regulator.

The bell jar and its attachments thus form a small furnace and this is immersed in an outer vessel containing a known quantity of water at a known temperature.

104 Meatturemi'ut of Iddt [oh.

The fuel is then ignited (this being done by means of a small piece of platinum wire heated by an electric curi^nt) and the flow of oxygen is regulated so that the "flue gases" formed by the burning fuel bubble slowly up through the water. Thus they give out their heat to the water.

When the fuel has completely burned itself out the water is allowed to flow inside the jar so that we can be quite sure that all the heat generated has been absorbed by the water. The temperature is then taken and the calorific value is calculated as shewn below.

Mass of water = Mw lbs.

Water equivalent of calorimeter: Bell-jar, etc. = Mc lbs.

(This water equivalent is usually given by the makers of the calorimeter, but of course it can be calculated or determined by experiment. In this case a record would be kept for future use.)

Total equivalent mass of water = Mw + Mc = M lbs.

Original temperature of water = t° F.

Final temperature of water after fuel has been burned = t° F.

Therefore heat received by water = M x (ig — ^i) b.th.u.

Mass of fuel burned = P lbs.

Therefore if M {t^ — tj) b.th.u. were given by the

combustion of P lbs. — ^A, — - British thermal units

would be given by 1 lb. in burning.

And this is the calorific value of the fuel.

The results could all be taken with metric units, if desired, and the calorific value in calories per gramme could be determined.

IX j Measurement of Heat 105

The following table shews the calorific values of some fuels in British thermal units per lb. of fuel.

Methylated alcohol

11,320

Steam coal

15,600

Benzol

17,750

Bituminous coal

14,600

Petrol

20,000

Coal gas (London)

500 B.TH.U.

Paraffin oil

19,000

per cubic foot

Two values for the Specific Heat of a Gas. The

reader has already noted that two values are quoted on page 98 for the specific heat of air. It has been found that if the volume is kept constant the gas ab- sorbs less heat per degree of temperature than it does if it is allowed to expand at constant pressure. This is an interesting and important matter to engineers. The explanation is to be found in the fact that if the gas expands it has to do work in pushing back the surround- ing atmosphere, just as if it were pushing back a piston in an engine cylinder. This work is done at the expense of some of the heat which is being given to it and there- fore we have to give it more heat to raise its temperature through each degree than would be necessary if it was not expanding. The additional heat represents the work which the gas is doing in -expanding.

The methods for the determination of these specific heats are of a very refined order, and the details cannot be dealt with in this little volume.

106 M(<if<i(i< iiif III ill' Ilfttf [<n. IX

EXAMPLES

1. Find the heat necessary to raise the temperature of 3-5 lbs. of water from 59° F. to 212° F. If the same amount of heat be given to 17-5 lbs. of iron at 59° F. to what temperature would it be raised ? The specific heat of iron = 0-1 12/

2. 4-8 lbs. of copper at 177° F. are plunged in 3 lbs. of water at 60° F. and the resulting temperature of the mixture is 75-6° F. What is the specific heat of the copper?

3. A copper calorimeter (sp. heat -094) weighs 0*2 lb. and contains 0-75 lb. of water at 50° F. What is the water equivalent of the calorimeter and the total equivalent weight of water of calorimeter and contents? It is found that when 2-5 lbs. of iron at some unknown temperature are placed in the calorimeter the temperature rises to 60° F. How much heat did the iron give out and what must its original temperature have been? Sp. heat dl iron -3 01 12.

4. If all the heat given by 0-02 lb. of coal of calorific value 15,600 B.TH.u. per lb. were given to a glass vessel containing 3 lbs. of water at 60° F. (the glass vessel weighing 2-7 lbs. and having a specific heat of 0-19) to what temperature would it be raised?

5. A mass of 200 grammes of copper of specific heat 0-1 is heated to 100° C. and placed in 100 grammes of alcohol at 8° C. contained in a copper calorimeter of 25 grammes mass : the tem- perature rises to 28° C. What is the specific heat of the alcohol ?

6. 3-5 lbs. of water at 200° F. are mixed with 5 lbs. of water at 60° F. the cold water being poured into the hot which is con- tained in a copper calorimeter of 1 lb. weight and specific heat 0-1. Find the temperature of the mixture (a) neglecting the calorimeter, (6) taking the calorimeter into account.

CHAPTER X

FUSION AND SOLIDIFICATION

The third important effect of heat upon matter is that known as a change of physical condition such, for example, as the change of a substance from the sohd to the Hquid form. If such a change is effected without producing any change in the chemical constitution of the substance it is called a physical cJiange of state. When heat is given to ice it changes to water (which is chemically the same thing) and if more heat be given it will ultimately change again to steam, which again has the same chemical composition.

When heat is applied to coal chemical changes take place, and the same applies to many other substances. But if no chemical change is produced then the physical change is produced : and we shall only consider such change in this volume.

Melting Point of a Solid. The temperature at which a solid melts — that is to say changes into the liquid form — is called the melting point of that solid. Different substances have different melting points as the following table shews.

Iron (wrought) 1600° C.

Ice

0°C.

Aluminium

600

Antimony Bismuth ...

440 26.5

Brass

1015

Carbon . . .

3500

Copper . . . Gold

1050 1250

Iridium . . .

1950

Iron (cast) ..

1100

Lead

325

Mercury

. - 39-5

Platinum . .

. 1700

Silver

. 1000

Steel

. 1350

Tin

. 231

Tungsten . .

. 3200

Zinc

. 420

!()}{ Fusion it 11(1 Solidification [CH.

The melting point is usually a well-defined tempera- ture though there are some substances like glasg, for example, which become plastic and slowly change to the fluid state. It is difficult to determine the exact melting point of such a substance.

The solidifying point or freezing point of a liquid is that temperature at which it changes from liquid to soUd. This temperature is the same as the melting point. That is to say, ice melts at 0° C. and water freezes at 0° C.

Heat required to melt a solid. In order to melt a soHd it is not enough to heat it to its melting point. Additional heat must be given when this temperature is reached and it will be found that such heat does not produce any increase in temperature until the whole of the soUd is melted. If some ice be placed in a vessel and the vessel be heated over a furnace it will be found that

(a) the temperature of ice will increase if it were below 0° C. at the start :

(6) when it reaches 0° C. it will remain stationary until every particle of ice is melted :

(c) when the ice is all melted then the temperature of the water will rise.

During this experiment the ice and water must be kept thoroughly stirred.

The same thing exactly applies to the melting of any other substance though equal masses of different substances do not all require the same quantity of heat energy to melt them after the melting point has been reached. In this respect ice requires more heat than is required by any of the metals given in the above list. The reader must think this over carefully and see that he understands exactly what is meant.

x] Fusion and Solidification 109

Latent Heat of Fusion. The quantity of heat necessary to change a unit mass of a solid at its melting POINT to liquid at the same temperature is called the latent heat of fusion of that substance.

For example the latent heat of fusion of ice (on the British system of measurements) is 144. That is to say 144 b.th.u. of heat are required to change 1 lb. of ice at 32° F. into 1 lb. of water at 32° F. Conversely when 1 lb. of water at 32° F. freezes to ice at the same temperature it must give up 144 b.th.u. of heat.

On the metric system the quantity of heat necessary to melt 1 gramme of ice at 0" C. and change it to water at 0° C. is 80 calories.

The latent heat of fusion of a few substances is shewn below.

Latent heat in British thermal units per lb. of substance.

Ice ...

144

Bismuth

23

Zinc ...

i51

Sulphur

17

Silver

38

Lead . . .

9-6

Tin ...

25-6

Mercury

5

- An interesting experiment, which illustrates how melting points may be determined and demonstrates at the same time the fact that heat is absorbed or yielded by a substance in changing its physical state, may be performed by placing some paraffin wax, or better still some naphthalene, in a boiling tube and heating this tube in a water bath. The bath should be heated until all the wax has melted. A thermometer should then be placed in the hquid formed and the bath allowed to cool. Readings of the thermometer

110

Fiution and Solidiji cation

[CH.

should then be taken at regular intervals of time — say every half-minute. It will be noted that the thermo- meter falls steadily to a certain "temperature after which it remains stationary (or in some cases it may even rise again slightly) for several minutes. During this stationary period it will be noted that the wax is solidifying, and when it has all become solid the tem- perature will start to fall again.

Fig. 38 gives two graphs (one for wax and the other for naphthalene) shewing how the temperature falls with

90

80

70

V

\

\

\

■

\

0

y

\

\

\

\^

\

<^

\

N

v/

:^

k

\

\

^\

^-7v

\

^

^t(

^

X'

\^\

^

^

^

2 4 6 8

10 Mini

12

ites

14

16

18

20 22 24

Vm.

38

the time. The melting point is that temperature at which the cooUng temporarily ceases. The explanation lies in the fact that on solidifying the substance gives out heat, and this heat suffices to prevent the temperature from falling. In the case of substances with a more defined melting point than wax the heat given out on soUdifi- cation will cause the temperature to increase. This is shewn on the naphthalene graph. It should be pointed

x] Fusion and Solidification 111

out that the melting point of the naphthalene is given by the horizontal part of the graph.

We may also compare, roughly, the latent heat of each substance by noting the length of time during which the temperature remains practically constant. The longer the time the greater must be the quantity of heat given out. Of course, the reader will see that such comparison could only be made if equal masses of substances were used and allowed to cool under equal conditions. This in turn would mean that only sub- stances with approximately equal melting points could be compared in this way. From our curves we can see that the naphthalene has a greater latent heat than the wax.

Change of volume with change of state. It is found that some substances, like water, increase in volume in passing from the hquid to the solid state. That is to say a given mass of the substance will have a greater volume in the solid state than in the liquid state at the same temperature. We say that such substances expand on solidification. Other substances contract on solidifi- cation.

This is important to engineers for many reasons. Firstly, whenever a casting is made we have a liquid changing to solid. If that substance contracts on solidification the chances are that we shall not be able to get a good casting- — that is to say a well defined casting — because the metal will shrink away from the sand mould. If we can use a metal which expands slightly on solidification, or one which does not change in volum.e, we shall get sharp castings which will not need so much machining. Metals like copper and iron contract on solidification. Antimony and bismuth

112 Ftmon ami Solidificafion [CH.

expand on solidification. Some alloys like type-metal (an alloy of lead, tin and antimony) expand on solidifi- cation. In fact that is the sole reason why this par- ticular alloy is used for making type. Some readers may have seen castings which were ready for immediate assembling on being taken out of the sand. They are sharply defined, have smooth surfaces, and do not require any machining.

Secondly, if there is going to be any appreciable change of volume then account will have to be taken of this in the size of the pattern. The volume of the pattern will be the volume of the molten metal.

Again, especially in the case of larger castings, the metal nearer to the sand will solidify first, so that when the inner portions sofidify stresses are produced due to internal contractions or expansions, and these may cause the casting to break.

It is well known that water expands on sofidification. Water pipes are burst in winter time by that expansion. It is that same expansion which breaks up the soil for the farmer.

Determination of the Latent Heat of Fusion of ice. A calorimeter, of known water equivalent, containing a known mass of water at a known temperature is taken, and into this are dropped small pieces of dry ice (each piece must be carefully dried with flannel). This process is continued until the temperature of water has been reduced several degrees and when all the pieces of ice which have been introduced are seen to be melted the temperature is taken. The calorimeter and its contents are weighed again so that the mass -of ice which has been melted may be determined. From this the latent heat may be calculated.

x] Fusion and Solidification 113

The heat given out = (total equivalent mass of water) x (fall in its temperature).

The heat received = (mass of ice x latent heat of fusion) + (mass of . ice x rise in temperature from melting point to final temperature).

It will be seen that unless the temperature of the water is reduced to the melting point then the ice will receive heat firstly to melt it and secondly to heat the melted ice up to the final temperature of the water in the calorimeter.

Since the heat received = heat given out,

the latent heat is easily determined.

In performing the experiment it is well to start with the temperature of the water a few degrees above and to stop adding ice when it is the same number of degrees below the temperature of the room. The pieces of ice should be small and clean, and they should not be touched by the naked fingers.

Solution: Freezing mixtures. Whenever a solid dissolves in a liquid without producing any kind of chemical change the temperature of the liquid is reduced. A chemical change always generates heat : and thus when a solid is dissolved in a liquid and pro- duces a chemical combination the liquid will be heated if the chemical change is greater than the physical change and vice versa.

A mixture of salt and pounded ice or snow falls to a temperature as low as — 22° C. or — 7-6° F., according to the proportions of ice and salt.

Effect of Pressure on the Melting Point. The temperature at which a solid melts is only slightly affected by pressure. Ordinary changes in atmospheric pressure do not produce any measurable effect upon

V. Y, 8

114 i'nsiiui iind So/if/t/ica/ ioti |('H, X

the melting point, but it greater pressures be applied it is found that

(a) substances which expand on solidification have their melting points lowered by an increase in pressure, and

(6) substances which contract on solidification have their melting points raised by an increase in pressure.

That is to say ice can be melted by the application of great pressure, but of course the water so formed will be below the temperature of the freezing point and will freeze again at once when the pressure is released.

The making of a snowball ; the freezing together of two coUiding icebergs ; the progress of glaciers, are all explained by this.

EXAMPLES

1. How much heat would be necessary to heat up 3 lbs. of ice from a temperature of 10° F. to its melting point, to melt it, and to heat the water to the boiling point ? The specific heat of ice is 0-5 and its latent heat is 144 on the BritLsh system.

2. Compare the quantities of heat necessary to melt 4 lbs. of each of the following substances assuming thai they are all at' 32° F. to start with : ice, silver and lead. See pages 107 and 109 for melting points and latent heats, and page 98 for specific heats.

3. A cavity is made in a large block of ice and into it is put an iron sphere at a temperature of 1000° F. The iron weighs 0-64 lb. and its specific heat is 0-112. How much water will be formed in the cavity?

4. How many heat units on the c.g.s. system would be given out by half a litre of water in cooling down from 15° C. and freezing at 0° C. ? If this heat were given to 1 lb. of lead at 15° C. to what temperature would it be raised ? (Melting point, 325° C. : specific heat, 031 : latent heat, 9-6.)

CHAPTER XI

VAPORISATION

Just as a solid may be changed to the Hquid form by the apphcation of heat so can a hquid be changed to the gaseous form. This change of physical state is called vaporisation, the reverse change (from gas to liquid) being called condensation.

Vaporisation can take place either by the process known as evaporation or by the process of boiling or ebullition. These processes differ from one another. Evaporation takes place at all temperatures but it only takes place from the surface of a liquid. If equal quantities of water are placed in different vessels — one an open shallow dish, the other a tall narrow flower vase, for example — and left over night in the same room after having been weighed, it will be found next morning that the shallow vessel has lost more weight than the other one. We all know how a cork in a bottle will prevent evaporation : how an imperfect cork is a useless thing in a scent or other spirit bottle.

Ebullition or boiling will only take place at one definite temperature for a given liquid at a given pressure, and it takes place throughout the whole mass of the Uquid.

Boiling Point. We will deal with ebullition first. A hquid is said to be boifing when bubbles of vapour

8—2

IIU VnjHfn'siifioii [CH.

fomied at the bottom of the vessel rise up throughout the mass of the hquid and "burst" into tlie space above. Such bul)bles must not be confused with the more minute air bubbles which may rise up as soon as heat is supplied.

As soon as the liquid commences to boil its tempera- ture tvill cease to rise. The temperature of the hquid when this happens will be the boiUng point of that liquid : the temperature of the vapour in the space above will be the boihng point of that liquid which is formed by the condensation of the vapour. For example, if we boil some salt water we shall find that the temperature of the hquid is higher than that of the vapour above it. As we know, the vapour is steam and it will condense to water. Therefore the tempera- ture of the vapour is the boiling point of water: but the temperature of the hquid is the boiling point of that particular sample of salt water.

As a general rule if the hquid is of the same chemical composition as the vapour above it we take the tem- perature of the vapour, because the boiling point of a hquid is shghtly affected by mechanical impurities and by the material of the containing vessel.

Effect of Pressure on the Boiling Point. If we test the boiling point of a hquid on different days we shall find that it varies and that it is sHghtly higher when the barometer is higher. This suggests that the boiling point is affected by pressure. Complete in- vestigation leads to the discovery that a given hquid may be made to boil at any temperature within wide limits and that an increase in pressure raises the boiling point of all liquids whilst a decrease in pressure lowers the boihng point.

I

XI]

Vaporisation

117

The reader naturally enquires what is the boiling point of a Uquid? The answer is that we must define the boiling point of a given liquid as the temperature at which it boils at some definite pressure, and that the boiling points of all liquids should be taken at that pressure. The pressure chosen for this purpose is the normal atmospheric pressure- — that is to say the pres- sure of the atmosphere when the barometric height is 30 inches of mercury. This pressure is sometimes called a pressure of 1 atmosphere and is equivalent to 14-7 lbs. per square inch. Thus the boiling point of water is 100° C. or 212° F. when it is boiled in a vessel open to the atmosphere and the barometer stands at 30 inches.

If the water be boiled in a vessel which can be closed - — like the boiler shewn in Fig. 39— it will be found that, as the steam pressure inside increases, the boiling point will rise as shewn by the thermometer. The pres- sure can be determined by means of a pressure gauge, either of a direct reading pattern or of the pattern shewn in the figure. This is a U-tube having fairly long limbs. Mercury is put into this and when it has the same level in each limb then the pressure of the steam must be equal to that of the atmosphere. As the steam pressure increases the mercury will be forced down the

Fig. 39

118

VaporisaUon

[CH.

left and up the right limb and the steam pressure will then be greater than the atmospheric pressure by an amount represented by the difference in level of the mercury in each hmb. That is to say, if the difference is 6 inches and the atmospheric pressure is 30 inches then the steam pressure must be equivalent to that produced by a 36 inch column of mercury. Thus the relationship between the pressure of the steam and its temperature can be determined within the ranges possible with the apparatus.

Fig. 40 is an illustration of a converse experiment. It shews how water may boil at a lower temperature than 100° C. by reducing the pressure upon it. Some water is put into a round-bottomed flask and boiled. When it is boiling and steam is issuing freely we know that all the air has been driven out of the flask. The flame is removed and a cork with a thermometer is fitted. Then some cold water is squeezed out of a sponge on to the flask and it is noticed that the water inside at once ^'J^- *^

begins to boil again. The colder the water in the sponge the more vigorous will be the boihng of the water inside the flask, but of course the thermometer will indicate a rapidly falling temperature.

Obviously the cold water will cause some of the steam inside to condense : this condensation will reduce the pressure : this reduction will lower the boiling point

Hi=

^^ 1

XI]

Vaporisation

119

and the water will boil. There is always the risk of the flask breaking in this experiment, and it should be made of good quality glass, and of the shape shewn.

Temperature of steam at different pressures. The graph shewn as Fig. 41 indicates the temperature of

400 350 300 250 200

,-^

^

/

/

/

/

/

100

0

5

0 K

)0 1

50 2(

)0 2>

30 3C

0

Pressure in lbs. per sq. inch Fig. 41

steam at various pressures. At atmospheric pressure, 14-7 lbs. per square inch, the temperature of the steam is 212° F. At a pressure of 150 lbs. per square inch it is 358° F. : at 200 lbs. per square inch it is 381° F. and

1 20 Vaporisation [oh.

at 300 lbs. pressure it is 417° F. The average working steam pressures lie between 150 and 200 lbs. per square inch. Since the relationship between pressure and temperature can be obtained from the above graph, and since the relationship between the height of a place above sea level and the atmospheric pressure at that place compared with sea level pressure can also be obtained from a similar graph, it is quite obvious that height above sea level may be measured by finding the boiling point of water at various heights.

Evaporation. As we have said before this process goes on at all temperatures but only from the surface of a liquid. Our common experiences have taught us that some liquids evaporate much more quickly than others. We all know that petrol, scent, alcohol and benzoline will evaporate very quickly indeed, and we know the necessity for well-fitted stoppers for the vessels containing such liquids. We also know from our own experiences how water will evaporate or dry up more quickly on some days than on others. We know too that it is not entirely a question of temperature. We can think of hot close days in summer when water will not dry up at all. On such days the atmosphere is said to be saturated with water vapour : it cannot hold any more, and consequently no more evaporation of water can take place. That will not affect the evapora- tion of other liquids : but if the atmosphere could become saturated with petrol vapour (we hope that it never will) then even petrol would cease to evaporate. That indeed is the secret of the cork in a bottle. The space in a bottle jibove the liquid soon becomes satu- rated ; and then the liquid cannot evaporate any more : but if there were no cork to the bottle then the vapour

XI J Vaporisation 121

would go out into the atmosphere in a vain attempt to saturate that.

Heat necessary for Evaporation. Although this process goes on quietly and at all temperatures yet heat is necessary for its accomplishment. If a little alcohol, or petrol, or, better still, ether be poured on to the hand a sensation of cold will be experienced. Yet if the tem- perature of the liquid be taken it will be found to be the same as that of the room in which it is. The sensation of cold is brought about by the fact that the liquid absorbs heat more or less rapidly from the hand in proportion to its rate of evaporation. Thus the ether will feel colder than the alcohol, which in turn will feel colder than water — though in fact all three will have practically the same temperature*.

The rate at which they evaporate depends upon their boiling point and upon the condition of the space above them. A liquid with a low boiling point will evaporate much more quickly than one with a high boiling point — other things being equal. Nevertheless the liquid will require heat and the greater its rate of evaporation the more heat it will need. Some readers may have been unfortunate enough to have had their gums frozen prior to a tooth extraction. The "freezing " is produced by the rapid evaporation of ether absorbing much heat from the gum.

The cooling effect produced by "fanning" the face is due to the fact that the fan is continually replacing

* When a liquid evaporates the portion of liquid remaining will generally have its temperature diminished. How much it is diminished will ' depend upon the quantity of liquid, the rate of evaporation and the rate at which it receives heat from external sources.

122 Vaj)orisafi(Hi [vH.

the air near to the face with comparatively fresh and unsaturated air so that evaporation of the moisture on the face can proceed more rapidly. This evaporation can only take place by absorbing heat from the face : hence the coohng sensation. The same thing applies to the common method of finding which way the wind blows : that is by holding a moistened finger in various directions. That direction in which it feels coldest is the direqtion from which the wind is proceeding.

Vapour Pressure. Every kind of vapour exerts some pressure. The pressure which it exerts depends upon the amount of vapour present and upon the temperature. If the temperature is constant then as more and more liquid evaporates the pressure of the vapour will increase until the space is saturated with that vapour. Thus it follows that at a given tempera- ture a particular vapour will exert a maximum pressure when the space is saturated.

But though a space may be saturated with one vapour it can hold other vapours. And the total pressure in any enclosed space will be the sum of all the pressures produced by the several vapours. (This is known as Dalton's law but it is only approximately true in most cases.)

If a space be saturated %ith vapour and the tem- perature be increased it will be found that the pressure increases — though not proportionately. It will also be found that when the vapour pressure is equal to that produced by 3.0 inches of mercury the temperature will be the boiling point of that substance.

And from this it has been shewn that a liquid will boil whenever the pressure acting upon it is equal to its saturated vapour pressure. Therefore we can boil

xi] Vaporisation 123

a liquid at any temperature provided that we can adjust the pressure upon it to equal that of its saturated vapour pressure at that temperature. The boiling point of a liquid may therefore be defined as that temperature at which its vapour pressure is equal to that of 30 inches of mercury.

Boyle's Law and Vapour Pressure. If a saturated vapour occupies a definite volume and we reduce the volume, then if Boyle's law were to hold good the pressure of the vapour would be increased thereby. Actually however nothing of the kind occurs. The saturated vapour pressure cannot be increased except by an increase of temperature. We find on reducing the volume that some of the vapour condenses : but the pressure remains the same. Boyle's law does not hold good !

An experiment was performed by Dalton to illus- trate this. He made an ordinary mercury barometer using a longer tube than usual and a longer cistern (Fig. 4:2, A). Then he introduced a drop of ether into the tube by means of a bent pipette. This rose to the top and immediately evaporated, the pressure of the vapour causing the mercury to fall a little (B). Then he introduced a little more ether and a further fall of the mercury resulted. . So he continued until he noticed that the ether ceased to evaporate, shewn by the appearance of a layer of ether Uquid on the top of the mercury (C). He then found that the introduction of more ether did not increase the pressure — the liiercury remained at the same height — but simply added to the quantity of ether liquid floating on top of the mercury. Then he lowered the barometer down into the cistern {D and E) thereby diminishing the volume of the space

Vnporixdt'um

[CH.

above the mercurv, but he found that the pressure was not alt<>red — shewn by tlie mercury remaining at the same level. At the same time he noticed that the quantity of liquid ether above the mercury increased. Then he gradually withdrew the tube out of the cistern so increasing the volume of the space above the mercury.

Fig. 42

But again he found that the pressure remained constant and that the quantity of liquid ether diminished. When he was able, to get the tube high enough so that all the liquid ether had disappeared {F) then he found a slight drop in pressure shewn by the mercury rising [O).

He thus found that so long as a space is saturated with vapour that vapour will not obey Boyle's law :

XI J Vajjorisation 125

that no change in pressure could be produced by altering the volume of the space so long as the space was saturated. He also found by further experiment that Boyle's law does not hold good even when a space is not saturated ; but that the further the space is from saturation the closer does it follow the law.

Temperature and Vapour Pressure. An increase in temperature will cause an increase in pressure in either a saturated or an unsaturated space.

If a space be unsaturated a decrease in temperature will also cause a decrease in pressure, but if the tempera- ture be lowered sufficiently (depending upon the vapour under experiment) the space will become saturated and some of the vapour will condense : but the pressure will decrease so long as the temperature is decreased.

Charles' law does not hold good : but it is approxi- mately true in the case of non-saturated spaces ; and the further the space is from saturation the closer does that space obey the law.

Latent Heat of Vaporisation. Heat is necessary to vaporise a liquid whether the process of vaporisation is that of evaporation or of ebullition. The number of units of heat required to change a unit mass of a liquid into the gaseous state without a change in temperature is called the latent heat of vaporisation of that liquid.

It has been found that this is not a constant quantity for a given substance : it depends upon the temperature at which vaporisation takes place. However, it is usual to speak of the latent heat of vaporisation of a substance as the quayitity of heat necessary to clmnge a unit mass of the liquid at its normal boiling point to vapour at the same temperature.

We are chiefly concerned with water and steam.

126 Voporisaffo)f [ch.

The latent heat of vaporisation oi uatei' — more com- monly called the latent heat of steam — is 066 British thermal units per pound, or 537 calories per gramme.

This means that in order to change 1 lb. of water at 212° F. into 1 lb. of steam at 212° F. we have to supply 966 British thermal units of heat. Conversely when 1 lb. of steam at 212° F. condenses to water at the same temperature it gives out 966 British thermal units.

Sensible Heat and Total Heat. If we have 1 lb. of water at 60° F. and we wish to convert it to steam at atmospheric pressure we shall have to give it heat

(1) to raise its temperature from 60° F. to 212° F. and

(2) to convert it from water at 212° F. to steam at 212° F.

For this we shall require (1) (212 — 60) x 1 units, and (2) 966 x 1 units, that is to say 1118 units in all.

The heat which produces a change in temperature is often called the sensible heat. In the case just quoted the sensible heat amounts to 152 units. The sum of the sensible heat and the latent heat is called the total heat.

Determination of the Latent Heat of Steam. In this measurement it is necessary to pass a known mass of dry steam into a calorimeter of known water equivalent containing a known mass of water at a known tempera- ture. This steam will heact the water and from the increase in temperature we can easily find how much heat the water and the calorimeter have received. Now all this must have been given out by the steam and it gave it (a) in condensing, (6) in cooling down from water at the boiling point to water at the final temperature of the calorimeter. As we can easily calculate this latter

xi] Vajmrisatio^i 127

amount, we have only to subtract it from the total heat received by the calorimeter and the remainder must represent the heat given out by the steam in condensing without change in temperature. We can then calculate how much a unit mass of steam would have given out and the latent heat of steam is deter- mined.

The usual method is as follows :

Weigh the inner vessel of the calorimeter.

Partially fill with water and weigh again.

From this get the weight of the water. ^ Add to this the water equivalent of the calorimeter.

Take the temperature of the water.

Then allow dry steam to pass into the water.

When the temperature of the water has risen some 20 degrees shut off the steam, stir well, and take the final temperature of the water in the calorimeter.

Weigh again so that you may get the mass of the steam condensed.

Calculate the value of the latent heat of steam.

The chief points of importance in the performance of this experiment are (a) to be sure that the steam which is passed into the calorimeter is quite dry and does not carry any water particles with it ; and (6) to prevent loss of heat due to radiation from the calori- meter. The steam may be made dry by using some kind of a steam dryer such as that shewn in Fig. 43. The loss of heat can be reduced to a minimum by arranging that the temperature of the water in the calorimeter shall be as much below the temperature of the room at the beginning of the experiment as it is above it at the end. Thus the loss and gain of heat will approxi- mately balance.

\'2i\

Viijutnsntitnt

[CH.

There is nothing difficult about the calculations. The only point which is likely to be overlooked is that the heat given out by each unit mass of steam in con- densing down to the final temperature is the total heat, and that this is the sum of the sensible heat and the latent heat.

Steam entry

Exhaust ^ for condensed water

Steam exit to Calorimeter

Fig. 43

Variation of Latent Heat of Steam with Temperature. Regnault fovmd that the latent heat of steam was not a constant quantity. He found that as the tempera- ture at which the steam is produced increases (due to increased pressure upon the water) the latent heat decreases and vice versa.

It has been shewn that the variation is approxi- mately as follows: for each degree F. above the boiling point (212°) the latent heat of steam is dimin- ished by 0-695 b.th.u. per lb. of steam, and for each degree F. below the boiling point the latent heat is increased by 0-695 b.th.u.. per lb. of steam.

xi] Vaporisation 129

Thus at a temperature of 300° F. the latent heat of steam will be 966 less 0-695 unit for each degree above 212°. That is to say the latent heat will be

966 - (88 X 0-695) - 966 - 61-16 = 904-84-

Similarly at a temperature of 180° F. (that is under reduced pressure) the latent heat of steam would be 966 + {(212 - 180) X 0-695} = 988-24.

On the metric system of units the variation is 0-695 calorie per gramme for each degree Centigrade above or below the boiling point (100° C).

Pressure and Temperature of Saturated Steam.

Although we know that an increase in pressure causes an increase in temperature of the steam above boiling water yet no definite law connecting these quantities has been expressed. Certain empirical formulae have been deduced to enable one to calculate the pressure at some known temperature or vice versa, and these formulae are often used for the purpose.