Question

For an ideal gas, the molecular partition function in the canonical ensemble, that is proportional to the system volume (V), is the

• A. vibrational partition function
• B. rotational partition function
• C. electronic partition function
• D. translational partition function

Hint:

Partition function separates into translational, rotational, vibrational, electronic parts.
Only translational motion depends on system volume; others depend on temperature and level spacings.

Answer 1

The Correct Option is D

Step 1: Recall definition. The molecular partition function is the product of contributions from translational, rotational, vibrational, and electronic motions: \[ q = q_{trans} \cdot q_{rot} \cdot q_{vib} \cdot q_{elec}. \]
Step 2: Translational partition function. For a particle in a box of volume \(V\), \[ q_{trans} = \left( \frac{2\pi m k_B T}{h^2} \right)^{3/2} V. \] Thus, it is directly proportional to system volume \(V\).
Step 3: Others. Rotational, vibrational, and electronic partition functions depend only on temperature and energy-level spacings, not on system volume. Conclusion: The translational partition function is the one proportional to \(V\).