$A$ diatomic gas molecule has translational,rotational,and vibrational degrees of freedom. The ratio ${C_P}/{C_V}$ is

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma$,the change in internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $p$,is

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_{P}$ and $C_{V}$ respectively. If $\gamma = \frac{C_{P}}{C_{V}}$ and $R$ is the universal gas constant,then $C_{V}$ is equal to

If $C_p$ and $C_v$ denote the specific heat of nitrogen at constant pressure and constant volume respectively,then

On giving an equal amount of heat at constant volume to $1 \, mol$ of a monoatomic and a diatomic gas,the rise in temperature $(\Delta T)$ is more for:

The value of the gas constant $(R)$ calculated from the perfect gas equation is $8.32 \ J/mol \cdot K$,whereas its value calculated from the knowledge of $C_P$ and $C_V$ of the gas is $1.98 \ cal/mol \cdot K$. From this data,the value of $J$ is ......... $J/cal$.