UPSC Combined Geo-Scientist, Mains · 2025 · Mains Paper II
Q1(f). Z > 1 and f > P for the gas P(Vm − b) = RT
Question
For a gas obeying the equation of state P(Vm − b) = RT, (i) Z (compressibility factor) > 1 and (ii) f (fugacity) > P. Justify with reasons.
Answer in brief
(i) Z = 1 + bP/RT > 1, b being the positive excluded volume; (ii) f = P ebP/RT > P, because b > 0.
Key points
- (i) PVm = RT + Pb ⇒ Z = 1 + bP/RT; b is the excluded volume, so b > 0 and Z > 1.
- (ii) ln(f/P) = ∫₀ᴾ (b/RT) dP = bP/RT > 0 ⇒ f = P ebP/RT > P.
- Reason: only repulsion acts. Molecules are pushed apart, so the escaping tendency exceeds the ideal value: fugacity coefficient ϕ = f/P > 1.
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.
Coversfugacityfugacity coefficientcompressibility factorexcluded volumeequation of state
All parts of Question 1
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