Question

Let \(γ_1\) be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a mono-atomic gas and \(γ_2\) be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, \(γ_1/γ_2\) is

• A. \(27/35\)
• B. \(35/27\)
• C. \(25/21\)
• D. \(21/25\)

Hint:

\(\gamma = 1+\frac{2}{f}\); monatomic \(f=3\), rigid diatomic \(f=5\).

Answer 1

The Correct Option is C

Step 1: Plan:
Use molar heat capacities directly.

Step 2: Steps:
Monatomic: $C_V = \frac32R$, $C_p = \frac52R$, $\gamma_1 = \frac53$. Rigid diatomic: $C_V = \frac52R$, $C_p = \frac72R$, $\gamma_2 = \frac75$.
Divide: $\frac53\times\frac57 = \frac{25}{21}$. The values $\frac{27}{35}$, $\frac{35}{27}$ and $\frac{21}{25}$ arise from wrong pairings or inversions.

Final Answer:
The ratio is $\frac{25}{21}$, option (C). \[ \boxed{\frac{25}{21}} \]