Page:Elementary Text-book of Physics (Anthony, 1897).djvu/241

§ 317] change of temperature is that experienced in passing from the isothermal $$OB$$ to the isothermal which passes through $$A.$$ The heat abstracted to produce the diminution of pressure $$\Delta p$$ is therefore $$C_{v}. \frac{\Delta p}{\delta p}. \Delta t.$$ Now the internal energy of the gas in the condition represented by $$A$$ depends only on its temperature and is independent of the way in which that condition is reached. The work done on the gas in its change from $$O$$ to $$A$$ does depend on the way in which the change is effected, but the difference between the work done on it during the first operation and that done on it during the second operation is an infinitesimal of the second order, represented by the area $$OCA$$ (§ 232), and may be neglected. The quantities of heat abstracted during the two operations may therefore be set equal, so that we have $$C_{p} \Delta t = C_{v}\frac{\Delta p}{\delta p} \Delta t,$$ and hence by the equation already obtained.

It has been shown that the Telocity of sound in any medium is equal to the square root of the quotient of the elasticity divided by the density of the medium; that is, $$velocity = \sqrt{\frac{E}{D}}\cdot$$ In the progress of a sound-wave the air is alternately compressed and rarefied, the compressions and rarefactions occurring in such rapid succession that there is no time for any transfer of heat. If this equation be applied to air, the $$E$$ becomes $$E_{h},$$ or the elasticity under the condition that no heat enters or escapes. Since we know the density of the air and the velocity of sound, $$E_{h}$$ can be computed. In § 105 it is shown that $$E_{t}$$ is numerically equal to the pressure; hence we have the values of the two elasticities of air, and, as seen above, their ratio is the ratio of the two specific heats of air.

217. Examples of Energy absorbed by Vaporization.—When a liquid boils, its temperature remains constant, however intense the source of heat. This shows that the heat applied to it is expended in producing the change of state. Heat is absorbed during