Question

In non-rigid diatomic molecules with an additional vibrational mode: \( C_P \) and \( C_V \) become:

• A. \( 81C_V^2 = 49C_P^2 \)
• B. \( 49C_V^2 = 25C_P^2 \)
• C. \( 49C_P^2 = 81C_V^2 \)
• D. \( 25C_V^2 = 49C_P^2 \)

Hint:

Use \( \gamma = \frac{C_P}{C_V} \) and express as square ratio to compare heat capacities.

Answer 1

The Correct Option is A

We use: \[ \gamma = \frac{C_P}{C_V},\quad \Rightarrow \frac{C_P^2}{C_V^2} = \gamma^2 \] For diatomic gas with vibration, \( \gamma = \frac{7}{5} \Rightarrow \left( \frac{C_P}{C_V} \right)^2 = \left( \frac{7}{5} \right)^2 \Rightarrow 49C_V^2 = 25C_P^2 \Rightarrow 81C_V^2 = 49C_P^2 \]