Page:Elementary Text-book of Physics (Anthony, 1897).djvu/239

§ 215] to describe in detail the means by which the effects of the disturbing causes have been determined or eliminated.

The specific heat of a gas at constant volume is generally determined from the ratio between it and the specific heat at constant pressure. The first direct determination of this ratio was accomplished by Clement and Desormes. It is now most commonly determined from the velocity of sound (§§ 135, 216).

215. Work Done by the Expansion of a Gas.— It was shown by Joule that when a gas expands without doing external work, its temperature remains practically constant. His experiment consisted in allowing gas compressed within a reservoir to flow into another reservoir in which a vacuum had been made. The reservoirs were immersed in the water of a calorimeter; it was found that in these circumstances the expansion of the gas was not attended either by the evolution or absorption of heat. As the gas had done no external work during the expansion, this proved that its energy remained unchanged. The energy of a gas is therefore a function of its temperature alone.

If the temperature of a unit mass of gas be raised 1° while its volume is kept constant, the quantity of heat $$C_{v},$$ the specific heat at constant volume, must enter the gas. If its temperature be raised by the same amount while it is allowed to expand under constant pressure and to do work $$W$$ by that expansion, a quantity of heat $$C_{p},$$ the specific heat at constant pressure, must be used. Since the gas is at the same temperature at the end of each of these operations, its energy must be the same in both cases, and the difference between the quantities of heat employed, or $$C_{p} - C_{v},$$ must be equal to the work $$W$$ done by the expansion.

The experiments of Joule and Thomson, which proved that the experiment of Joule just described was not sufficiently sensitive to yield an exact result, and that the temperature of a gas really falls slightly when it expands without doiug external work, do not seriously invalidate the conclusion just drawn; they merely prove that some internal work is done in the gas during its expansion. This internal work is so small in amount that it may be neglected in most cases.