Question

The internal energy of one mole of a rigid diatomic gas at absolute temperature \( T \) is:

• A. \( 3RT \)
• B. \( \frac{5}{2} RT \)
• C. \( \frac{3}{2} RT \)
• D. \( \frac{1}{2} RT \)

Hint:

For rigid diatomic gases, the degrees of freedom are 5 (3 translational + 2 rotational), leading to: \[ U = \frac{5}{2} nRT \]

Answer 1

The Correct Option is B

The internal energy of a gas is given by: \[ U = \frac{f}{2} nRT \] For one mole (\( n = 1 \)) of a rigid diatomic gas, only translational and rotational degrees of freedom contribute. The degree of freedom for such a gas is: \[ f = 5 \] Thus, the internal energy is: \[ U = \frac{5}{2} RT \] Conclusion Thus, the correct answer is: \[ \frac{5}{2} RT \]