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A pure gas obeys the equation of state given by $$\dfrac{PV}{RT} = 1 + \dfrac{BP}{RT}$$ where $P$ is the pressure, $T$ is the absolute temperature, $V$ is the molar volume of the gas, $R$ is the universal gas constant, and $B$ is a parameter independent of $T$ and $P$. The residual molar Gibbs energy, $G^R$, of the gas is given by the relation $$\dfrac{G^R}{RT} = \int _0^P (Z-1) \dfrac{dP}{P}$$ where $Z$ is the compressibility factor and the integral is evaluated at constant $T$. If the value of $B$ is $1 \times 10^{-4} m^3 \: mol^{-1}$, the residual molar enthalpy (in $J \: mol^{-1})$ of the gas at $1000 \: kPa$ and $300 \: K$ is

  1. $100$
  2. $300$
  3. $2494$
  4. $30000$
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