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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 · 2016 · Mains Paper II

Q1(a). Virial equation

Question

What is the virial equation of state for real gases? Express the van der Waals equation in virial form. Discuss the physical significance of the virial coefficients.

Answer in brief

Z=1+B(T)/Vₘ+C(T)/Vₘ²+⋯; for a van der Waals gas, B=b-a/(RT) and C=b².

Key points

  • The compressibility factor is Z=pVₘ/(RT). An ideal gas has Z=1.
  • Expand p=RT/(Vₘ-b)-a/Vₘ² in powers of 1/Vₘ: Z=1/(1-b/Vₘ)-a/RTVₘ=1+(b-a/(RT))/Vₘ+b²/Vₘ²+⋯.
  • The second virial coefficient measures pair-interaction effects.

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(a), 2016 Mains Paper II: solution pages 1 and 2
Solution pages 1 and 2 of 19
Read the whole 2016 solution2016 question paper

CoversVirial equationGaseous state

All parts of Question 1