For a gas,the difference between the two specific heats is $4150 \ J \ kg^{-1} \ K^{-1}$ and the ratio of the two specific heats is $1.4$. What is the specific heat of the gas at constant volume in units of $J \ kg^{-1} \ K^{-1}$?

$50 \, cal$ of heat is required to raise the temperature of $1 \, mol$ of an ideal gas from $20^{\circ} C$ to $25^{\circ} C$,while the pressure of the gas is kept constant. The amount of heat required to raise the temperature of the same gas through the same temperature range at constant volume is ........ $cal$ $(R = 2 \, cal / mol \cdot K)$.

Molar specific heat at constant volume,for a non-linear triatomic gas is (vibration mode neglected).

For a rigid diatomic molecule,the universal gas constant $R = n C_P$,where $C_P$ is the molar specific heat at constant pressure and $n$ is a number. Hence,$n$ is equal to

Molar specific heat of oxygen at constant pressure $C_p = 7.2 \, cal/mol \cdot ^\circ C$ and $R = 8.3 \, J/mol \cdot K$. At constant volume,$5 \, mol$ of oxygen is heated from $10^\circ C$ to $20^\circ C$. The quantity of heat required is approximately ........ $cal$.

The ratio of the specific heats $\frac{C_{p}}{C_{v}}=\gamma$,in terms of degrees of freedom $(n)$ is