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 $(C^{A}_{V}$ and $C^{B}_{V})$ 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 $= 7$
$\therefore C^{A}_{v}=\frac{f_{A}}{2} R=\frac{5}{2} R \,\&\,C^{B}_{v}=\frac{f_{B}}{2} R=\frac{7}{2}R$
$\therefore \frac{C^{A}_{v}}{C^{B}_{v}}=\frac{5}{7}$