Theory of Heat (Maxwell, 4th edition)/Chapter 3
CHAPTER III.
CALORIMETRY.
Having explained the principles of Thermometry, or the method of ascertaining temperatures, we are able to understand what we may call Calorimetry, or the method of measuring quantities of heat.
When heat is applied to a body it produces effects of various kinds. In most cases it raises the temperature of the body; it generally alters its volume or its pressure, and in certain cases it changes the state of the body from solid to liquid or from liquid to gaseous.
Any effect of heat may be used as a means of measuring quantities of heat by applying the principle that when two equal portions of the same substance in the same state are acted on by heat in the same way so as to produce the same effect, then the quantities of heat are equal.
We begin by choosing a standard body, and defining the standard effect of heat upon it. Thus we may choose a pound of ice at the freezing point as the standard body, and we may define as the unit of heat that quantity of heat which must be applied to this pound of ice to convert it into a pound of water still at the freezing point. This is an example of a certain change of state being used to define what is meant by a quantity of heat. This unit of heat was brought into actual use in the experiments of Lavoisier and Laplace.
In this system a quantity of heat is measured by the number of pounds (or of grammes) of ice at the freezing point which that quantity of heat would convert into water at the freezing point.
We might also employ a different system of measurement by defining a quantity of heat as measured by the number of pounds of water at the boiling point which it would convert into steam at the same temperature.
This method is frequently used in determining the amount of heat generated by the combustion of fuel.
Neither of these methods requires the use of the thermometer.
Another method, depending on the use of the thermometer, is to define as the unit of heat that quantity of heat which if applied to unit of mass (one pound or one gramme) of water at some standard temperature (that of greatest density, 39° F. or 4° C., or occasionally some temperature more convenient for laboratory work, such as 62° F. or 15° C.), will raise that water one degree (Fahrenheit or Centigrade) in temperature.
According to this method a quantity of heat is measured by the quantity of water at a standard temperature which that quantity of heat would raise one degree.
All that is assumed in these methods of measuring heat is that if it takes a certain quantity of heat to produce a certain effect on one pound of water in a certain state, then to produce the same effect on another similar pound of water will require as much heat, so that twice the quantity of heat is required for two pounds, three times for three pounds, and so on.
We have no right to assume that because a unit of heat raises a pound of water at 39° F. one degree, therefore two units of heat will raise the same pound two degrees; for the quantity of heat required to raise the water from 40° to 41° may be different from that which raised it from 39° to 40°. Indeed, it has been found by experiment that more heat is required to raise a pound of water one degree at high temperatures than at low ones.
But if we measure heat according to either of the methods already described, either by the quantity of a particular kind of matter which it can change from one easily observed state to another without altering its temperature, or by the quantity of a particular kind of matter which it can raise from one given temperature to another given temperature, we may treat quantities of heat as mathematical quantities, and add or subtract them as we please.
We have, however, in the first place to establish that the heat which by entering or leaving a body in any manner produces a given change in it is a quantity strictly comparable with that which melts a pound of ice, and differs from it only by being so many times greater or less.
In other words, we have to show that heat of all kinds, whether coming from the hand, or hot water, or steam, or red-hot iron, or a flame, or the sun, or from any other source, can be measured in the same way, and that the quantity of each required to effect any given change, to melt a pound of ice, to boil away a pound of water, or to warm the water from one temperature to another, is the same from whatever source the heat comes.
To find whether these effects depend on anything except the quantity of heat received—for instance, if they depend in any way on the temperature of the source of heat—suppose two experiments tried. In the first a certain quantity of heat (say the heat emitted by a candle while an inch of candle is consumed) is applied directly to melt ice. In the second the same quantity of heat is applied to a piece of iron at the freezing point so as to warm it, and then the heated iron is placed in ice so as to melt a certain quantity of ice, while the iron itself is cooled to its original temperature.
If the quantity of ice melted depends on the temperature of the source from whence the heat proceeds, or on any other circumstance than the quantity of the heat, the quantity melted will differ in these two cases; for in the first the heat comes directly from an exceedingly hot flame, and in the second the same quantity of heat comes from comparatively cool iron.
It is found by experiment that no such difference exists, and therefore heat, considered with respect to its power of warming things and changing their state, is a quantity strictly capable of measurement, and not subject to any variations in quality or in kind.
Another principle, the truth of which is established by calorimetrical experiments, is, that if a body in a given state is first heated so as to make it pass through a series of states defined by the temperature and the volume of the body in each state, and if it is then allowed to cool so as to pass in reverse order through exactly the same series of states, then the quantity of heat which entered it during the heating process is equal to that which left it during the cooling process. By those who regarded heat as a substance, and called it Caloric, this principle was regarded as self-evident, and was generally tacitly assumed. We shall show, however, that though it is true as we have stated it, yet, if the series of states during the process of heating is different from that during the process of cooling, the quantities of heat absorbed and emitted may be different. In fact heat may be generated or destroyed by certain processes, and this shows that heat is not a substance. By finding what it is produced from, and what it is reduced to, we may hope to determine the nature of heat.
In most of the cases in which we measure quantities of heat, the heat which we measure is passing out of one body into another, one of these bodies being the calorimeter itself. We assume that the quantity of heat which leaves the one body is equal to that which the other receives, provided, 1st, that neither body receives or parts with heat to any third body; and, 2ndly, that no action takes place among the bodies except the giving and receiving of heat.
The truth of this assumption may be established experimentally by taking a number of bodies at different temperatures, and determining first the quantity of heat required to be given to or taken from each separately to bring it to a certain standard temperature. If the bodies are now brought to their original temperatures, and allowed to exchange heat among themselves in any way, then the total quantity of heat required to be given to the system to bring it to the standard temperature will be found to be the same as that which would be deduced from the results in the first case.
We now proceed to describe the experimental methods by which these results may be verified, and by which quantities of heat in general may be measured.
In some of the earlier experiments of Black on the heat required to melt ice and to boil water, the heat was applied by means of a flame, and as the supply of heat was assumed to be uniform, the quantities of heat supplied were inferred to be proportional to the time during which the supply continued. A method of this kind is obviously very imperfect, and in order to make it at all accurate would need numerous precautions and auxiliary investigations with respect to the laws of the production of heat by the flame and its application to the body which is heated. Another method, also depending on the observation of time, is more worthy of confidence. We shall describe it under the name of the Method of Cooling.
ICE CALORIMETERS.
Wilcke, a Swede, was the first who employed the melting of snow to measure the heat given off by bodies in cooling. The principal difficulty in this method is to ensure that all the heat given off by the body is employed in melting the ice, and that no other heat reaches the ice so as to melt it, or escapes from the water so as to freeze it. This condition was first fulfilled by the calorimeter of Laplace and Lavoisier, of which the description is given in the Memoirs of the French Academy of Sciences for 1780. The instrument itself is preserved in the Conservatoire des Arts et Métiers at Paris.
This apparatus, which afterwards received the name of Calorimeter, consists of three vessels, one within another.
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Fig. 6.
The first or innermost vessel, which we may call the receiver, is intended to hold the body from which the heat to be measured escapes. It is made of thin sheet copper, so that the heat may readily pass into the second vessel. The second vessel, or calorimeter proper, entirely surrounds the first. The lower part of the space between the two vessels is filled with broken ice at the freezing (or melting) point, and the first vessel is then covered by means of a lid, which is itself a vessel full of broken ice. When the ice melts in this vessel, whether in the lower part or in the cover of the first vessel, the water trickles down and passes through a drainer, which prevents any ice from escaping, and so runs out into a bottle set to catch it. The third vessel, which we may call the ice jacket, entirely surrounds the second, and is furnished, like the second, with an upper lid to cover the second. Both the vessel and the lid are full of broken ice at the freezing point, but the water formed by the melting of this ice is carried off to a-vessel distinct from that which contains the water from the calorimeter proper.
Now, suppose that there is nothing in the receiver, and that the temperature of the surrounding air is above the freezing point. Any heat which enters the outer vessel will melt some of the ice in the jacket, and will not pass on, and no ice will be melted in the calorimeter. As long as there is ice in the jacket and in the calorimeter the temperature of both will be the same, that is, the freezing point, and therefore, by the law of equilibrium of heat, no heat will pass through the second vessel either outwards or inwards. Hence, if any ice is melted in the calorimeter, the heat which melts it must come from the receiver.
Let us next suppose the receiver at the freezing temperature; let the two lids be carefully lifted off for an instant, and a body at some higher temperature introduced into the receiver; then let the lids be quickly replaced. Heat will pass from the body through the sides of the receiver into the calorimeter, ice will be melted, and the body will be cooled, and this process will go on till the body is cooled to the freezing point, after which there will be no more ice melted.
If we measure the water produced by the melting of the ice, we may estimate the quantity of heat which escapes from the body while it cools from its original temperature to the freezing point. The receiver is at the freezing point at the beginning and at the end of the operation, so that the heating and subsequent cooling of the receiver does not influence the result.
Nothing can be more perfect than the theory and design of this apparatus. It is worthy of Laplace and of Lavoisier, and in their hands it furnished good results.
The chief inconvenience in using it arises from the fact that the water adheres to the broken ice instead of draining away from it completely, so that it is impossible to estimate accurately how much ice has really been melted.
To avoid this source of uncertainty, Sir John Herschel proposed to fill the interstices of the ice with water at the freezing point, and to estimate the quantity of ice melted by the contraction which the volume of the whole undergoes, since, as we shall afterwards see, the volume of the water is less than that of the ice from which it was formed. I am not aware that this suggestion was ever developed into an experimental method.
Bunsen,[1] independently, devised a calorimeter founded on the same principle, but in the use of which the sources of error are eliminated, and the physical constants determined with a degree of precision seldom before attained in researches of this kind.
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Fig. 7.
Bunsen's calorimeter, as devised by its author, is a small instrument. The body which is to give off the heat which is to be measured is heated in a test-tube placed in a current of steam of known temperature. It is then dropped, as quickly as may be, into the test-tube T of the calorimeter, which contains water at 0° C. The body sinks to the bottom and gives off heat to the water. The heated water does not rise in the tube, for the effect of heat on water between 0° C. and 4° C. is to increase its density. It therefore remains surrounding the body at the bottom of the tube, and its heat can escape only by conduction either upwards through the water, or through the sides of the tube, which, being thin, afford a better channel. The tube is surrounded by ice at 0° C. in the calorimeter, C, so that as soon as any part of the water in the tube is raised to a higher temperature, conduction takes place through the sides, and part of the ice is melted. This will go on till everything within the tube is again reduced to 0° C., and the whole quantity of ice melted by heat from within is an accurate measure of the heat which the heated body gives out as it cools to 0° C.
To prevent any exchange of heat between the calorimeter C and surrounding bodies, it is placed in a vessel S filled with snow gathered when new fallen and free from smoke. This substance, unless the temperature of the room is below 0° C., soon acquires and long maintains the temperature of 0° C.
In preparing the calorimeter, it is filled with distilled water, from which every trace of air must be expelled by a careful process of boiling. If there is air in the water, the process of freezing expels it and produces bubbles of air, the volume of which introduces an error of measurement. The lower part of the calorimeter contains mercury, and communicates with a bent tube also containing mercury. The upper part of this tube is bent horizontally, and is carefully calibrated and graduated. As the mercury and the vessel are always at the temperature 0° C., they are of constant volume, and any changes in the position of the mercury in the graduated tube are due to the melting of ice in the calorimeter, and the consequent diminution of volume of the mass of ice and water in it.
The motions of the extremity of the column of mercury being proportional to the quantities of heat emitted from the test-tube into the calorimeter, it is easy to see how quantities of heat may be compared. In fact, Bunsen has made satisfactory determinations of the specific heat of those rare metals, such as indium, of which only a few grammes have been obtained.
To prepare the calorimeter for use, ice must be formed in the calorimeter round the test-tube. For this purpose, Bunsen causes a current of alcohol, cooled below 0° C. by a freezing mixture, to flow to the bottom of the test-tube and up along its sides. In this way the greater part of the water in the calorimeter is soon frozen. When the apparatus has been left for a sufficient time in the vessel containing snow, the temperature of this ice rises to 0° C., and the apparatus is ready for use. A great many experiments may be made after one freezing of the water.[2]
METHOD OF MIXTURE.
The second calorimetric method is usually called the Method of Mixture. This name is given to all the processes in which the quantity of heat which escapes from one body is measured by the increase of temperature it produces in another body into which it escapes. The most perfect method of ensuring that all the heat which escapes from the one body passes into the other is to mix them, but in many cases to which the method is now applied this cannot be done.
We shall illustrate this method by a few experiments, which can be performed by the student without any special apparatus. A few experiments of this kind actually performed by himself will give the student a more intelligent interest in the subject, and will give him a more lively faith in the exactness and uniformity of nature, and in the inaccuracy and uncertainty of our observations, than any reading of books, or even witnessing elaborate experiments performed by professed men of science.
I shall suppose the student to have a thermometer, the bulb of which he can immerse in the liquids of which the temperature is to be measured, and I shall suppose the graduation of the thermometer to be that of Fahrenheit, as it is the most common in this country.
To compare the effects of heat on water and on lead, take a strip of sheet lead, weighing, say, one pound, and roll it into the form of a loose spiral, so that when it is dropped into water the water may play round every part of it freely.
Take a vessel of a convenient shape, such that the roll of lead when placed in the vessel will be well covered with a pound of water.
Hang up the lead by a fine string and dip it in a saucepan of boiling water, and continue to boil it till it is thoroughly heated. While this is going on weigh out a pound of cold water in your vessel, and ascertain its temperature with the thermometer. Then lift the roll of lead out of the boiling water, hold it in the steam till the water is drained off, and immerse it as quickly as possible in the cold water in the vessel. By means of the string you may stir it about in the water so as to bring it in contact with new portions of the water, and to prevent it from giving its heat directly to the sides of the vessel.
From time to time observe the temperature of the water as indicated by the thermometer. In a few minutes the temperature of the water will cease to rise, and the experiment may then be stopped and the calculation begun.
I shall suppose (for the sake of fixing our ideas) that the temperature of the water before the hot lead was put in was 57° F., and that the final temperature, when the lead ceased to impart heat to the water, was 62° F. If we take as our unit of heat that quantity of heat which would raise a pound of water at 60° F. one degree, we have here five units of heat imparted to the water by the lead.
Since the lead was for some time in boiling water, and was afterwards held in the steam, we may assume its original temperature to be 212° (this, however, should be tested by the thermometer). During the experiment the lead cooled 150°—from 212° to 62°—and gave out, as we have seen, five units of heat to the water. Hence the difference of the heat of a pound of lead at 212° and at 62° is five units; or the same quantity of heat which will heat a pound of water five degrees from 57° to 62° will heat a pound of lead 150 degrees from 62° to 212°. If we assume, what is nearly though not exactly true, that the quantity of heat required to heat the lead is the same for each degree of rise of temperature, then we might say that to raise a pound of lead five degrees requires only one thirtieth part of the heat required to raise a pound of water five degrees.
We have thus made a comparison of the effects of heat on lead and on water. We have found that the same quantity of heat would raise a pound of lead through thirty times as many degrees as it would raise a pound of water, and we have inferred that to produce any moderate change of temperature on a pound of lead requires one-thirtieth of the heat required to produce the same change on an equal weight of water.
This comparison is expressed in scientific language by saying that the capacity of lead for heat is one-thirtieth of that of an equal weight of water.
Water is generally taken as a standard substance with which other substances are compared, and the fact which we have stated above is expressed in a still more concise manner by saying that the specific heat of lead is 1/30.
The fact that when equal weights of quicksilver and water are mixed together the resulting temperature is not the mean of the temperatures of the ingredients was known to Boerhaave and Fahrenheit. Dr. Black, however, was the first to explain this phenomenon and many others by the doctrine which he established, that the effect of the same quantity of heat in raising the temperature of the body depends not only on the amount of matter in the body, but on the kind of matter of which it is formed. Dr. Irvine, Black's pupil and assistant, gave to this property of bodies the name of Capacity for Heat. The expression Specific Heat was afterwards introduced by Gadolin, of Abo, in 1784.
I think we shall secure accuracy, along with the greatest conformity to established custom, by defining these terms thus:
DEFINITION OF THE CAPACITY OF A BODY.
The capacity of a body for heat is the number of units of heat required to raise that body one degree of temperature.
We may speak of the capacity for heat of a particular thing, such as a copper vessel, in which case the capacity depends on the weight as well as on the kind of matter. The capacity of a particular thing is often expressed by stating the quantity of water which has the same capacity.
We may also speak of the capacity for heat of a substance, such as copper, in which case we refer to unit of mass of the substance.
DEFINITION OF SPECIFIC HEAT.
The Specific Heat of a body is the ratio of the quantity of heat required to raise that body one degree to the quantity required to raise an equal weight of water one degree.
The specific heat therefore is a ratio of two quantities of the same kind, and is expressed by the same number, whatever be the units employed by the observer, and whatever thermometric scale he adopts.
It is very important to bear in mind that these phrases mean neither more nor less than what is stated in these definitions.
Irvine, who contributed greatly to establish the fact that the quantity of heat which enters or leaves a body depends on its capacity for heat multiplied by the number of degrees through which its temperature rises or falls, went on to assume that the whole quantity of heat in a body is equal to its capacity multiplied by the total temperature of the body, reckoned from a point which he called the absolute zero. This is equivalent to the assumption that the capacity of the body remains the same from the given temperature downwards to this absolute zero. The truth of such an assumption could never be proved by experiment, and its falsehood is easily established by showing that the specific heat of most liquid and solid substances is different at different temperatures.
The results which Irvine, and others long after him, deduced by calculations founded on this assumption are not only of no value, but are shown to be so by their inconsistency with each other.
We shall now return to the consideration of the experiment with the lead and water, in order to show how it can be made more accurate by attending to all the circumstances of the case. I have purposely avoided doing so at first, as my object was to illustrate the meaning of 'Specific Heat.'
In the former description of the experiment it was assumed, not only that all the heat which escapes from the lead enters the water in the vessel, but that it remains in the water till the conclusion of the experiment, when the temperatures of the lead and water have become equalised.
The latter part of this assumption cannot be quite true, for the water must be contained in a vessel of some kind, and must communicate some of its heat to this vessel, and also must lose heat at its upper surface by evaporation, &c.
If we could form the vessel of a perfect non-conductor of heat, this loss of heat from the water would not occur; but no substance of which a vessel can be formed can be considered even approximately a non-conductor of heat; and if we use a vessel which is merely a slow conductor of heat, it is very difficult, even by the most elaborate calculations, to determine how much heat is taken up by the vessel itself during the experiment.
A better plan is to use a vessel which is a very good conductor of heat, but of which the capacity for heat is small, such as a thin copper or silver vessel, and to prevent this vessel from parting rapidly with its heat by polishing its outer surface, and not allowing it to touch any large mass of metal, but rather giving it slender supports and placing it within a metal vessel having its inner surface polished.
In this way we shall ensure that the heat shall be quickly distributed between the water and the vessel, and may consider their temperatures at all times nearly equal, while the loss of heat from the vessel will take place slowly and at a rate which may be calculated when we know the temperature of the vessel and of the air outside.
For this purpose, if we intended to make a very elaborate experiment, we should in the first place determine the capacity for heat of the vessel by a separate experiment, and then we should put into the vessel about a pound of warm water and determine its temperature from minute to minute, while at the same time we observe with another thermometer the temperature of the air in the room. In this way we should obtain a set of observations from which we might deduce the rate of cooling for different temperatures, and compute the rate of cooling when the vessel is one, two, three, &c., degrees hotter than the air; and then, knowing the temperature of the vessel at various stages of the experiment for finding the specific heat of lead, we should be able to calculate the loss of heat from the vessel due to the cooling during the continuance of the experiment.
But a much simpler method of getting rid of these difficulties is by the method of making two experiments—the first with the lead which we have described, and the second with hot water, in which we endeavour to make the circumstances which cause the loss of heat as similar as we can to those in the case of the lead.
For instance, if we suppose that the specific gravity of lead is about eleven times that of water, if instead of a pound of lead we use one-eleventh of a pound of water, the bulk of the water will be the same as that of the lead, and the depth of the water in the vessel will be equally increased by the lead and the water.
If we also suppose that the specific heat of lead is one-thirtieth of that of water, then the heat given out by a pound of lead in cooling 150° will be equal to the heat given out by one-eleventh of a pound of water in cooling 55°.
Hence, if we take one-eleventh of a pound of water at 55° above 62°, that is at 117°, and pour it into the vessel with the water as before at 57°, we may expect that the level of the water will rise as much as when the hot lead was put in, and that the temperature will also rise to about the same degree. The only difference between the experiments, as far as the loss of heat is concerned, is, that the warm water will raise the temperature of the cold water in a much shorter time than the hot lead did, so that if we observe the temperature at the same time after the mixture in both cases, the loss by cooling will be greater with the warm water than with the hot lead.
In this way we may get rid of the chief part of the difficulty of many experiments of comparison. Instead of making one experiment, in which the cooling of the lead is compared with the heating of the water and the vessel, including an unknown loss of heat from the outside of the vessel, we make two experiments, in which the heating of the vessel and the total loss of heat shall be as nearly as possible the same, but in which the heat is furnished in the one case by hot lead, and in the other by warm water. The student may compare this method with the method of double weighing invented by Père Amiot, but commonly known as Borda's method, in which first the body to be weighed, and then the weights, are placed in the same scale, and weighed against the same counterpoise.
We shall illustrate this method by finding the effect of steam in heating water, and comparing it with that of hot water. Take a kettle, and make the lid tight with a little flour and water, and adapt a short india-rubber tube to the spout, and a tin or glass nozzle to the tube. Make the water in the kettle boil, and when the steam comes freely through the nozzle dip it in cold water, and you will satisfy yourself that the steam is rapidly condensed, every bubble of steam as it issues collapsing with a sharp rattling noise.
Having made yourself familiar with the general nature of the experiment of the condensation of steam, you may proceed to measure the heat given out to the water. For this purpose, put some cold water in your vessel, say about three-quarters of a pound. Weigh the vessel and water carefully, and observe the temperature of the water; then, while the steam flows freely from the nozzle, condense steam in the water for a short time, and remove the nozzle; observe the temperature and weigh the water in its vessel again, taking note of the time of the experiment.
Let us suppose the original weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
5,000 grains | |
Weight after the condensation of steam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
5,100 grains | |
Hence the weight of steam condensed is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
100 grains | |
Temperature of water at first . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
55° F. | |
Temperature at the end of experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
77° F. | |
Rise of temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
22° | |
Let us now make a second experiment, as like the first as we can, only differing from it by the use of hot water instead of steam to produce the rise of temperature.
It is impossible in practice to ensure that everything shall be exactly the same, but after a few trials we may select a method which will nearly, if not quite, fulfil the conditions.
Thus it is easy to bring the vessel and cold water to the same weight as before, namely, 5,000 grains; but we shall suppose the temperature now to be 56° F. instead of 55°. We now pour in water at 176° F. gradually, so as to make this experiment last about as long as the first, and we find that the temperature is now 76°, and the weight 6,000 grains. Hence 1,000 grains of water cooling 100° raise the vessel and its contents 22°.
Assuming that the specific heat of water is the same at all temperatures, which is nearly, though by no means exactly, true, the quantity of heat given out by the water in the second experiment is equal to what would raise 100,000 grains of water one degree.
In the experiment with the steam the temperatures were nearly though not exactly equal, but the rise of temperature was greater in the proportion of 22 to 20. Hence we may conclude that the quantity of heat which produced this heating effect in the experiment with steam was greater than in the experiment with water in the same proportion. This makes the heat given out by the steam equal to that which would raise 110,000 grains of water one degree.
This was done by the condensation and subsequent cooling of 100 grains of steam. Let us begin with the heat given out by the 100 grains of water at 212° F., into which the steam is condensed. It is cooled from 212° to 77° or 135°, and gives out therefore an amount of heat which would raise 13,500 grains of water one degree. But the whole effect was 110,000, so that there is an amount of heat which would raise 96,500 grains of water one degree, which must be given out during the condensation of the steam, and before the cooling begins. Hence each grain of steam in condensing gives out as much heat as would raise 965 grains of water 1° F. or 536 grains 1° Centigrade.
The fact that steam at the boiling point gives out a large quantity of heat when it is condensed into water which is still at the same temperature, and the converse fact that in order to convert water at the boiling temperature into steam of the same temperature a large quantity of heat must be communicated to it, was first clearly established by Black in 1757.
He expressed it by saying that the latent heat of steam is 965° F., and this form of expression is still in use, and we should take it to mean neither more nor less than what we have just stated.
Black, however, and many of his followers, supposed heat to be a substance which when it makes a thing hot is sensible, but which when it is not perceived by the hand or the thermometer still exists in the body in a latent or concealed state. Black supposed that the difference between boiling water and steam is, that steam contains a great deal more caloric than the hot water, so that it may be considered a compound of water and caloric; but, since this additional caloric produces no effect on the temperature, but lurks concealed in the steam ready to appear when it is condensed, he called this part of the heat latent heat.
In considering the scientific value of Black's discovery of latent heat, and of his mode of expressing it, we should recollect that Black himself in 1754 was the discoverer of the fact that the bubbles formed when marble is put into an acid consist of a real substance different from air, which, when free, is similar to air in appearance, but when fixed may exist in liquids and in solids. This substance, which we now call carbonic acid, Black called fixed air, and this was the first gaseous body distinctly recognised as such. Other airs or gases were afterwards discovered, and the impulse given to chemistry was so great, on account of the extension of the science to these attenuated bodies, that most philosophers of the time were of opinion that heat, light, electricity, and magnetism, if not the vital force itself, would sooner or later be added to the list. Observing, however, that the gases could be weighed, while the presence of these other agents could not be detected by the balance, those who admitted them to the rank of substances called them imponderable substances, and sometimes, on account of their mobility, imponderable fluids.
The analogy between the free and fixed states of carbonic acid and the sensible and latent states of heat encouraged the growth of materialistic phrases as applied to heat; and it is evident that the same way of thinking led electricians to the notion of disguised or dissimulated electricity, a notion which survives even yet, and which is not so easily stripped of its erroneous connotation as the phrase 'latent heat.' It is worthy of remark that Cavendish, though one of the greatest chemical discoverers of his time, would not accept the phrase 'latent heat.' He prefers to speak of the generation of heat when steam is condensed, a phrase inconsistent with the notion that heat is matter, and objects to Black's term as relating to an hypothesis depending on the supposition that the heat of bodies is owing to their containing more or less of a substance called the matter of heat; and, as I think Sir Isaac Newton's opinion that heat consists in the internal motion of the particles of bodies much the most probable, I chose to use the expression, "heat is generated."'[3]
We shall not now be in danger of any error if we use latent heat as an expression meaning neither more nor less than this:
Definition.—Latent heat is the quantity of heat which must be communicated to a body in a given state in order to convert it into another state without changing its temperature.
We here recognise the fact that heat when applied to a body may act in two ways—by changing its state, or by raising its temperature—and that in certain cases it may act by changing the state without increasing the temperature.
The most important cases in which heat is thus employed are—
1. The conversion of solids into liquids. This is called melting or fusion. In the reverse process of freezing or solidification heat must be allowed to escape from the body to an equal amount.
2. The conversion of liquids (or solids) into the gaseous state. This is called evaporation, and its reverse condensation.
3. When a gas expands, in order to maintain the temperature constant, heat must be communicated to it, and this, when properly defined, may be called the latent heat of expansion.
4. There are many chemical changes during which heat is generated or disappears.
In all these cases the quantity of heat which enters or leaves the body may be measured, and in order to express the result of this measurement in a convenient form, we may call it the latent heat required for a given change in the substance.
We must carefully remember that all that we know about heat is what occurs when it passes from one body to another, and that we must not assume that after heat has entered a substance it exists in the form of heat within that substance. That we have no right to make such an assumption will be abundantly shown by the demonstration that heat may be transformed into and may be produced from something which is not heat.
Regnault's method of passing large quantities of the substance through the calorimeter will be described in treating of the properties of gases, and the Method of Cooling will be considered in the chapter on Radiation.