e diatomic gases, such
as H2, O2, N2, CO, &c., and has nearly the same value for each gas. They
also indicate that it is much larger, and increases considerably with
rise of temperature, in the case of more condensible vapours, such as
Cl2, Br2, or more complicated molecules, such as CO2, N2O, NH3, C2H4.
The direct determination of the specific heat at constant volume is
extremely difficult, but has been successfully attempted by Joly with
his steam calorimeter, in the case of air and CO2. Employing pressures
between 7 and 27 atmospheres, he found that the specific heat of air
between 10 deg. and 100 deg. C. increased very slightly with increase of
density, but that of CO2 increased nearly 3% between 7 and 21
atmospheres. The following formulae represent his results for the
specific heat s at constant volume in terms of the density d in gms. per
c. c.:--

Air, s = 0.1715 + 0.028d,

CO2, s = 0.165 + 0.213d + 0.34d^2.

S 18. _Ratio of Specific Heats._--According to the elementary kinetic
theory of an ideal gas, the molecules of which are so small and so far
apart that their mutual actions may be neglected, the kinetic energy
of translation of the molecules is proportional to the absolute
temperature, and is equal to 3/2 of pv, the product of the pressure
and the volume, per unit mass. The expansion per degree at constant
pressure is v/[theta] = R/p. The external work of expansion per degree
is equal to R, being the product of the pressure and the expansion,
and represents the difference of the specific heats S - s, at constant
pressure and volume, assuming as above that the internal work of
expansion is negligible. If the molecules are supposed to be like
smooth, hard, elastic spheres, incapable of receiving any other kind
of energy except that of translation, the specific heat at constant
volume would be the increase per degree of the kinetic energy namely
3pv/2[theta] - 3R/2, that at constant pressure would be 5R/2, and the
ratio of the specific heats would be 5/3 or 1.666. This appears to be
actually the case for monatomic gases such as mercury vapour (Kundt
and Warburg, 1876), argon and helium (Ramsay, 1896). For diatomic or
compound gases Clerk Maxwell supposed that the molecule would also
possess energy of rotation, and endeavoured to prove that in this case
the energy would be equally divided between the six degrees of
freedom, three of translation and three of