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Indian Forest Service (Mains)

Chemistry optional

  • 2 papers
  • 200 marks each
  • 3 h per paper

Paper I covers physical and inorganic chemistry.

Indian Forest Service (Mains), Chemistry optional · 2021 · Paper I

Q4(b). Canonical partition function and heat capacity

Question

Give the classical statistical mechanical definition of the canonical partition function, Q. What is the relationship between thermodynamic Helmholtz free energy, F, and Q? Using these expressions show that the heat capacity at constant volume, CV, is given by CV = kT[∂²(T ln Q)/∂T²]V.

Answer in brief

For the classical canonical ensemble, Q = (N!h³ᴺ)⁻¹ ∫ e−H/kT d³ᴺp d³ᴺq, and F = −kT ln Q.

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Topic notes: statistical thermodynamics, the Boltzmann distribution, partition functions and the Sackur–Tetrode equation, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coverscanonical partition functionHelmholtz free energyheat capacity Cvstatistical thermodynamicsF = −kT ln Q

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