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

The relation between $\mathrm{\gamma }$ and number of vibrational modes v is

$$\begin{gathered} \mathrm{\gamma }=\frac{4+\mathrm{v}}{3+\mathrm{v}} \\ \text{ Given }\mathrm{v}=24 \\ \therefore \mathrm{\gamma }=\frac{4+24}{3+24}=1.037 \end{gathered}$$