Question

What is the molar specific heat at constant volume $ C_V $ of a diatomic gas molecule if one additional vibrational degree of freedom is considered?

• A. \( \frac{5}{2} R \)
• B. \( \frac{6}{2} R \)
• C. \( \frac{7}{2} R \)
• D. \( \frac{9}{2} R \)

Hint:

Each vibrational mode contributes 2 degrees of freedom: one kinetic and one potential.

Answer 1

The Correct Option is C

For a diatomic gas without vibrational modes, the degrees of freedom (D.O.F) = 5. With one vibrational mode added (which contributes 2 degrees of freedom), total D.O.F becomes 7. According to the equipartition theorem: \[ U = \frac{7}{2} RT \] So, \[ C_V = \left( \frac{dU}{dT} \right) = \frac{7}{2} R \]