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: Key Formula:
\(\gamma = \frac{C_p}{C_V} = 1 + \frac{2}{f}\), where \(f\) is the number of degrees of freedom.

Step 2: Values:
Monatomic gas: \(f = 3\), so \(\gamma_1 = \frac53\).
Rigid diatomic gas: \(f = 5\), so \(\gamma_2 = 1 + \frac25 = \frac75\).

Step 3: Ratio:
\[ \frac{\gamma_1}{\gamma_2} = \frac{5/3}{7/5} = \frac{25}{21} \]

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