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UPSC Combined Geo-Scientist

Chemist

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

Mains Paper II covers physical chemistry.

UPSC Combined Geo-Scientist, Mains · 2019 · Mains Paper II

Q1(e). Volume independence of ideal-gas heat capacity

Question

Show that (∂ CV/∂ V)_(T,n)=0 for an ideal gas.

Answer in brief

Ideal-gas internal energy depends only on temperature, so its temperature derivative CV has no volume dependence.

Key points

  • Use (∂ U/∂ V)T=T(∂ p/∂ T)V-p. For p=nRT/V, the right side is T(nR/V)-nRT/V=0.
  • Therefore U=U(T,n) and CV=(∂ U/∂ T)_(V,n) is a function of T,n only.
  • More explicitly, interchange mixed derivatives: (∂ CV/∂ V)T=∂[(∂ U/∂ V)T]/∂ T=0. Temperature dependence of CV itself is still possible.

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

Model answer to Q1(e), 2019 Mains Paper II: solution pages 3 and 4
Solution pages 3 and 4 of 17
Read the whole 2019 solution2019 question paper

CoversVolume independence of ideal-gas heat capacityThermodynamics

All parts of Question 1