Question

The mean energy per molecule for a diatomic gas is:

• A. \( \frac{5}{2} k_B T \)
• B. \( \frac{3}{2} k_B T \)
• C. \( \frac{7}{2} k_B T \)
• D. \( \frac{6}{2} k_B T \)

Hint:

Diatomic gas → 5 degrees of freedom → energy = \( \frac{5}{2}k_B T \).

Answer 1

The Correct Option is A

Step 1: Degrees of freedom.
A diatomic gas has 5 degrees of freedom (3 translational + 2 rotational).

Step 2: Energy per degree of freedom.
Each degree contributes:
\[ \frac{1}{2}k_B T \]

Step 3: Total energy.
\[ E = \frac{f}{2}k_B T \]
\[ E = \frac{5}{2}k_B T \]

Step 4: Final conclusion.
\[ \boxed{\frac{5}{2}k_B T} \] Hence, correct answer is option (A).