Specific heat at constant pressure 0·2375 " " " volume 0·1683
Ratio between these numbers: 0·2375/0·1683 = 1·41
This ratio is termed the ratio between the specific heats of air, and such a ratio is represented usually by the letter =γ=.
But it is not necessary to determine both kinds of specific heat in order to arrive at a knowledge of the value of this ratio. One plan, adopted by Gay-Lussac and Désormes at the suggestion of Laplace,[28] is to actually measure the fall of temperature by allowing a known volume of gas, of which the weight can of course be deduced, to expand from a pressure somewhat higher than that of the atmosphere to atmospheric pressure. It is true that heat will rapidly flow in through the walls of the vessel; but by choosing a sufficiently large vessel, and surrounding its walls with badly-conducting material, the entry of heat will be so slow that it may, for practical purposes, be neglected. The number for this ratio, actually found by Gay-Lussac and Welters for air, was 1·376; but subsequent and more accurate experiments have given as a result 1·405, which is almost identical with that calculated above.
This method, however, can be employed only when an unlimited supply of gas is at disposal, for it entails the use of large vessels, and the compressed gas must be allowed to escape into the atmosphere, and is lost. There is, fortunately, another method by which the same results can be obtained, and which requires only a small amount of gas.
Sir Isaac Newton calculated that the velocity of sound in a gas was dependent on its pressure and on its density, in such a manner that
where _c_ stands for velocity (celerity), _p_ for pressure, and _d_ for density. When waves of sound are transmitted through air, the air is compressed in parts and rarefied in parts, in such a manner that compression follows rarefaction very rapidly, that part which is compressed at one instant being rarefied at the next, compressed again at a third, and rarefied at a fourth, and so on. Laplace was the first to point out that during such rapid changes of pressure as occur while a sound-wave is passing, the pressure will not rise proportionally to the density, as would be the case if Boyle’s law were followed; for on sudden rise of pressure the temperature of the compressed portion of the gas will be increased; and, correspondingly, on sudden fall of pressure, the wave of compression having passed, the temperature will fall. He showed that instead of two pressures being inversely proportional to their two volumes, under such circumstances, as they are according to Boyle’s law, or