GATE Thermodynamics and Statistical Mechanics: partition function, free energy, calculation of thermodynamic quantities – Previous Year Questions

5 GATE previous year questions on partition function, free energy, calculation of thermodynamic quantities (Thermodynamics and Statistical Mechanics, Physics) with answers and explanations, from every paper.

1. GATE 2022 PH Q36 (2 marks, Multiple choice) – A noninteracting spin-one gas has moment mu and B/(k BT)1. Find its mean magnetic moment.
2. GATE 2023 PH Q38 (2 marks, Multiple choice) – A harmonic oscillator has =2k BT/ in thermal equilibrium at temperature T. Which is its partition function?
3. GATE 2026 PH Q25 (1 mark, Multiple select) – Schematic variation of the specific heat Cp of an ideal gas of diatomic molecules with temperature T is shown in the figure below. For rotational…
4. GATE 2026 PH Q45 (2 marks, Multiple choice) – A gas of N classical particles that can occupy energy levels, ε1 and ε2 = ε1 + Δ is in equilibrium with a reservoir at temperature T. From the…
5. GATE 2024 PH Q59 (2 marks, Numerical answer) – An ideal gas has Q=1N![V/(T)3]N, where is thermal de Broglie wavelength. Use N!=N N-N. For density N/V=2.51025 m−3, e/(k BT)(T)-310-25 is m−3 (one…