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Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, $\frac{\gamma_1}{\gamma_2}$ is
The value of $\gamma\left(=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right),$ for hydrogen, hellium and another ideal diatomic gas $X$(whose molecules are not rigid but have an additional vibrational mode), are respectively equal to
A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gases are filled in left $(L)$ and right $(R)$ halves. The rms speed of the molecules in $L$ part is equal to the mean speed of molecules in the $R$ part. Then the ratio of the mass of a molecule in $L$ part to that of a molecule in $R$ part is