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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 · 2026 · Mains Paper II

Q1(e). Fugacity against pressure of a non-ideal gas

  • 5 marks
  • Topic: Thermodynamics
  • Answered
Question

With the help of the relation between fugacity (f) and pressure (P) of a non-ideal gas, mention the conditions when (i) f>P, (ii) f=P and (iii) f<P.

Answer in brief

f=φ P (φ = fugacity coefficient). (i) f>P (φ>1): repulsion dominates (high P). (ii) f=P (φ=1): ideal gas or P→0. (iii) f<P (φ<1): attraction dominates (moderate P).

Key points

  • the pressure the gas would need if it were ideal to have the same chemical potential.
  • Z>1 (repulsion) ⇒φ>1; Z<1 (attraction) ⇒φ<1; Z=1⇒φ=1. Also f/P→1 as P→0.

The full model answer

Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.

μ=μ^°+RTln(f)/(P^°); φ=∫₀^P(Z-1)/(P) dP

  • f is the effective pressure: the pressure the gas would need if it were ideal to have the same chemical potential.
  • Z>1 (repulsion) ⇒φ>1; Z<1 (attraction) ⇒φ<1; Z=1⇒φ=1. Also f/P→1 as P→0.
Model answer to Q1(e), 2026 Mains Paper II: solution page 5
Solution page 5 of 22
Read the whole 2026 solution2026 question paper

CoversfugacityFugacity against pressure of a non-ideal gas

All parts of Question 1