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GATE 2023 CY – Question 29

Physical Chemistry · Statistical Thermodynamics: Micro-canonical, Canonical and Grand canonical ensembles, Boltzmann distribution, Partition functions and thermodynamic properties. Statistical mechanics of non-interacting systems, ideal monoatomic, diatomic gases, translational, rotational, vibrational and electronic partition functions. · 1 mark · Multiple choice

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

  1. vibrational partition function
  2. rotational partition function
  3. electronic partition function
  4. translational partition function

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Correct answer: (D) translational partition function

Explanation

The translational states count grows with the available spatial volume. Explicitly, qtrans=V(2πmkBT/h²)^(3/2), so it is linear in V. Internal vibrational, rotational and electronic partition functions depend on their level spacings rather than container volume. **Answer: D**.