# 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 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/75 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/76 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/77 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/78 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/79 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/80 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/81 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/82 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/83 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/84 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/85 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/86 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/87 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/88 ​Page:Theory of Heat, James Clerk Maxwell, Fourth Edition.djvu/89 ​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.