GATE 2020 CH – Question 49
A pure gas obeys $PV/(RT)=1+BP/(RT)$, with molar V and constant B independent of T,P. Its residual Gibbs energy satisfies $G^R/(RT)=\int_0^P(Z-1)dP/P$ at constant T. For B = 10⁻⁴ m³/mol, P = 1000 kPa and T = 300 K, find residual molar enthalpy in J/mol.
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Correct answer: (A) 100
Explanation
Substitution gives $G^R/(RT)=\int_0^PB/(RT)dP=BP/(RT)$, so Gᴿ = BP. Residual enthalpy is $H^R=G^R-T(\partial G^R/\partial T)_P$. Because B is temperature-independent, the derivative is zero and Hᴿ = BP. In SI units this is $10^{-4}(10^6)=100$ J/mol, A.
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