At standard temperature and pressure $(STP)$,the density of a gas is $1.3 \ kg/m^3$ and the speed of sound in the gas is $330 \ m/s$. The degree of freedom of the gas is:

Calculate the total number of degrees of freedom of molecules of hydrogen in $1$ $cc$ of hydrogen gas at $NTP$.

For a gas having $X$ degrees of freedom,what is the value of $\gamma$ (where $\gamma$ is the ratio of specific heats,$\gamma = C_{P} / C_{V}$)?

Define degree of freedom.

Derive the equation for the internal energy of a gas in terms of its degrees of freedom.

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$. Molecules of the gas $A$ are rigid,and have a mass $m$. Molecules of the gas $B$ have an additional vibrational mode,and have a mass $\frac{m}{4}$. The ratio of the specific heats $(C_{v}^{A}$ and $C_{v}^{B})$ of gas $A$ and $B$,respectively,is