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Process Calculations
Laws of Thermodynamics
GATE 2020
Hard

A pure gas obeys PV/RT=1+BP/RT, where B is independent of T and P. The residual molar Gibbs energy is GR/RT=∫0^P (Z−1)dP/P at constant T. If B=1×10⁻⁴ m³/mol, the residual molar enthalpy (J/mol) of the gas at 1000 kPa, 300K is

  • 100
  • B300
  • C2494
  • D30000

Explanation

Z−1=BP/RT, so GR/RT=∫0^P(BP'/RT)dP'/P'=BP/RT ⟹ GR=BP (T-independent since B is T-independent). Then HR=GR+T·SR where SR=−(∂GR/∂T)P=0 (GR=BP has no T dependence), so HR=GR=BP=1×10⁻⁴×1,000,000=100 J/mol.

Source: GATE CH 2020 (2020)

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