Question

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$. Molecules of the gas A are rigid , and have an 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 :

• A. 5 : 9
• B. 7 : 9
• C. 3 : 5
• D. 5 : 7

Answer 1

Answer: (D)

Degree of freedom of a diatomic molecule if vibration is absent $=5$
Degree of freedom of a diatomic molecule if vibration is present $=7$
$\therefore C_v^A=\frac{f_A}{2}R=\frac{5}{2}R\&C_v^B=\frac{f_B}{2}R=\frac{7}{2}R$
$\therefore \frac{C_v^A}{C_v^B}=\frac{5}{7}$