The internal energy $(U)$,pressure $(P)$,and volume $(V)$ of an ideal gas are related as $U = 3PV + 4$. The gas is:

The ratio of specific heats at constant pressure and at constant volume is $\gamma$. To find out the degree of freedom,the expression is

If one mole of a polyatomic gas has two vibrational modes and $\beta$ is the ratio of molar specific heats for the polyatomic gas $\left(\beta=\frac{C_{P}}{C_{V}}\right)$,then the value of $\beta$ is:

$500 \text{ g}$ of a diatomic gas is enclosed at a pressure of $10^5 \text{ N m}^{-2}$. The density of the gas is $5 \text{ kg m}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator].

The mean kinetic energy of $1 \, mole$ of gas per degree of freedom (on the basis of kinetic theory of gases) is

What is the degree of freedom?