The ratio of the molar specific heat capacities of monatomic and diatomic gases at constant pressure is (in $: 7$)

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 ......... $J/cal$.

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a mono-atomic gas and $\gamma_2$ be the similar ratio of a diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $\gamma_1/\gamma_2$ is

$A$ gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume $(C_v)$ to the specific heat of gas at constant pressure $(C_p)$ will be.

The specific heat at constant volume for the monoatomic argon is $0.075 \, kcal/kg-K$,whereas its gram molecular specific heat $C_V = 2.98 \, cal/mole/K$. The mass of the argon atom is (Avogadro's number $= 6.02 \times 10^{23} \, molecules/mole$)

The amount of heat energy required to raise the temperature of $1 \ g$ of helium from $T_1 \ K$ to $T_2 \ K$ at $NTP$ is ........