W(T SM (T2— T) And from this we easily find W(T •M(T2—T) In the actual conduct of an experiment of this kind there are many difficulties to overcome, and many corrections to be estimated and ap plied. There is always more or less communi cation of heat between the apparatus and out side objects, and the heat that is given out by the cooling body warms not only the water, but also the containing vessel, the thermometers and the stirring apparatus.
In determining the specific heat of a body advantage is often taken of the known fact that the quantity of heat required to melt one pound of ice at 32° F. is approximately the same as the quantity of heat required to raise the tempera ture of one pound of water by 140° F. In the application of this fact to the determination of specific heats the body under investigation is surrounded by ice, and the number of units of heat that are given off is determined by observ ing the quantity of ice that is melted, and multiplying that quantity (as expressed in pounds) by 140. Bunsen devised a very delicate apparatus for the execution of this sort of measurement. In his instrument the body to he studied is placed in a cup-shaved depression in a glass vessel that is filled with ice and water, and which is entirely sealed, save for a grad uated capillary tube, one end of which enters the mixture of ice and water, while the other end projects into the air. The quantity of ice that is melted by the heat given off from the body is not directly observed, but is inferred from the change in volume of the ice-and-water mixture, as indicated by the motion of an index drop of mercury in the capillary tube; it being known that ice upon melting contracts by about one twelfth of its own volume.
The specific heat of a gas is defined in pre cisely the same way as the specific heat of any • other body; but in the case of gases it is neces sary to specify the way in which the change of temperature of the gas takes place. Thus we may heat a gas while we maintain its pressure constant (permitting the volume to increase as much as it will), or we may heat it while its volume is kept constant (the pressure mean while increasing). The specific heats obtained
under these two different conditions are quite different in numerical value, and they are dis tinguished respectively, as the "specific heat at constant pressure') and the "specific heat at con stant volume?' The specific heat of a gas at constant pressure may be determined with considerable accuracy by causing a stream of the gas to flow through a calorimeter, so that it ex periences a definite fall in temperature in its transit. The quantity of heat given up by the gas can be made to be very considerable (and hence easily measurable) by continuing the flow for a sufficient time; and to determine the spe cific heat at constant pressure, we then have merely to divide the total quantity of heat given out by the gas by the total mass of the gas that has been passed through the calorimeter, and again by the fall in temperature that the gas has experienced. The specific heat at constant volume is more difficult to obtain, and it has usually been determined by an indirect method, rather than by direct measurement. It can be determined directly, however, and apparently with considerable precision, by means of the Joly steam calorimeter.
Following are the specific heats of a number of substances; though it must be remembered that many of them are more or less uncertain, not only because they vary (in the case of solids) from one specimen to another, and from one temperature to another in all substances, but also because in their determination the ther mometric and calorimetric work has unfor tunately not always been beyond reproach.
In the foregoing table the results given for gases are the specific heats at constant pressure.
Consult Ganot,