If the molar specific heat at constant volume is $\frac{3R}{2}$,then the adiabatic index $\gamma$ is:

According to the law of equipartition of energy, the molar specific heat of a diatomic gas at constant volume, where the molecule has one additional vibrational mode, is:

$5$ moles of oxygen is heated at constant volume from $10^{\circ}C$ to $20^{\circ}C$. The change in the internal energy of the gas is (given $C_p = 8 \text{ cal/mole } ^{\circ}C$ and $R = 2 \text{ cal/mole } ^{\circ}C$ approximately).

The values of $C_P$ and $C_V$ for a gas were measured by three different students. The unit is $\text{cal/g mol-K}$. Which set is the most reliable?

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

The molar specific heat at constant pressure of an ideal gas is $(7/2)R$. The ratio of specific heat at constant pressure to that at constant volume is