A gas consisting of rigid diatomic molecules was expanded in a polytropic process so that the rate of collisions of the molecules against the vessel's wall did not change. Find the molar heat capacity of the gas in this process.

Explanation

If `alpha` is the polytropic index then
`pV^alpha =` constant, `TV^(alpha -1) =` constant
Now `(v')/(v') = (n')/(n) (lt v' gt)/(lt v gt) = (V)/(V') sqrt((T')/(T)) = (VT^(-1//2))/(V' T'^(-1//2)) = 1`
Hence `(1)/(alpha - 1) = -(1)/(2)`or `alpha = -1`
Then `C = (iR)/(2) + ( R)/(2) = 3 R`.