γ_A is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. γ_B is the specific heat ratio of polyatomic gas B…

$\displaystyle \gamma_{\mathrm{A}}$ is the specific heat ratio of monoatomic gas A having $\displaystyle 3$ translational degrees of freedom. $\displaystyle \gamma_{\mathrm{B}}$ is the specific heat ratio of polyatomic gas B having $\displaystyle 3$ translational, $\displaystyle 3$ rotational degrees of freedom and $\displaystyle 1$ vibrational mode. If $\displaystyle \frac{\gamma_A}{\gamma_B}=\left(1+\frac{1}{n}\right)$, then the value of $\displaystyle n$ is $\displaystyle \_\_\_\_$.