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Laws of Thermodynamics
GATE 2016
Hard
A gas follows the Clausius EOS P=RT/(v−b(T)), b(T)=b0+b1T, b0=4×10⁻⁵ m³/mol, b1=1.35×10⁻⁷ m³/mol·K. It is isothermally compressed from 5MPa to 15MPa at 400K. Using (∂h/∂P)T=v−T(∂v/∂T)P, the change in molar enthalpy (J/mol), rounded to 1 decimal place, is
400 J/mol(± 0.5 accepted)
Explanation
v=RT/P+b0+b1T, (∂v/∂T)P=R/P+b1. So (∂h/∂P)T=v−T(R/P+b1)=b0 (constant, the b1T terms cancel exactly). Δh=b0×(P2−P1)=4×10⁻⁵×10×10⁶=400 J/mol.
Source: GATE CH 2016 (2016)
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