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

When $40 \ J$ of heat is absorbed by a monatomic gas,the increase in the internal energy of the gas is (in $J$)

If $C_{p}$ and $C_{v}$ are molar specific heats of an ideal gas at constant pressure and volume respectively and $\gamma$ is $C_{p} / C_{v}$,then $C_{p} =$ (where $R$ is the universal gas constant).

The specific heat capacities of an ideal gas at constant pressure and at constant volume are $620 \ J \ kg^{-1} \ K^{-1}$ and $420 \ J \ kg^{-1} \ K^{-1}$ respectively. The density of the gas at $STP$ is approximately, (in $kg \ m^{-3}$)

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?

An ideal gas has molar heat capacity $C_V$ at constant volume. The gas undergoes a process where the temperature changes as $T=T_0(1+\alpha V^2)$, where $T$ and $V$ are temperature and volume respectively, and $T_0$ and $\alpha$ are positive constants. The molar heat capacity $C$ of the gas is given as $C=C_V+R f(V)$, where $f(V)$ is a function of volume. The expression for $f(V)$ is