Question

The molar specific heat capacity of a diatomic gas at constant pressure is \( C \). The molar specific heat capacity of a monatomic gas at constant volume is

• A. \( \frac{2C}{7} \)
• B. \( \frac{3C}{7} \)
• C. \( \frac{C}{7} \)
• D. \( \frac{4C}{7} \)

Hint:

For specific heat relations, remember \( C_P - C_V = R \) and apply ratio-based methods when comparing different gases.

Answer 1

The Correct Option is B

For a diatomic gas: \[ C_P = C_V + R \] Since \( C_P = C \), we get: \[ C_V = C - R \] For a monatomic gas: \[ C_V' = \frac{3}{2} R \] Using \( C_P = \frac{7}{2} R \), we write: \[ C_V' = \frac{3}{7} C \] Thus, the correct answer is \( \frac{3C}{7} \).