Q: One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas . what is the molar specific heat of the mixture at constant volume ?

Sol: The value of γ of a mixture is given by

$\large \frac{n_1 + n_2}{\gamma -1} = \frac{n_1}{\gamma_1 -1} + \frac{n_2}{\gamma_2 -1} $

$\large \frac{1 + 1}{\gamma -1} = \frac{1}{5/3 -1} + \frac{n_2}{7/5 -1} $

γ = 1.5

In general , $\large C_v = \frac{R}{\gamma -1} $

$\large C_v = \frac{R}{1.5 -1} $

C_{v} = 2 R

Hence , the specific heat of mixture is 2R