$\gamma_{A}$ is the specific heat ratio of monoatomic gas $A$ having 3 translational degrees of free

Question

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

Professor PC Thomas Classes · Answer

(3) : $\gamma_{A}$ monoatomic (3 translational degree)\ $\gamma_{B}$ polyatomic (3 translational +3 rotational +1 vibration)\ $\frac{\gamma_{A}}{\gamma_{B}}=\frac{f_{A}+2}{f_{A}} 	imes \frac{f_{B}}{f_{B}+2}$\ $=\frac{3+2}{3} 	imes \frac{7}{(7)+2}=\frac{35}{24}=\frac{1+1}{n}$\ $\because n=\frac{27}{8}=3.375 \approx 3$\ $	herefore \quad n=3$\