$A$ polyatomic ideal gas has $24$ vibrational modes. What is the value of $\gamma$ ?

Write the degree of freedom for a polyatomic gas.

For polyatomic gases,the ratio of molar specific heat at constant pressure to constant volume is $(f=$ degrees of freedom $)$

If the kinetic energy of a monoatomic gas molecule is $\frac{3}{2}PV$,then the kinetic energy of a diatomic gas molecule is:

For two different gases $X$ and $Y,$ having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{v_1}$ and $C_{v_2}$ respectively, for an adiabatic process, the $\ln P$ versus $\ln V$ graph is plotted as shown:

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