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Consider the van der Waals equation of state:

$$\left( P+\frac { { n }^{ 2 }a }{ { V }^{ 2 } } \right) \left( V-nb \right) =nRT$$

...where $P$ is the pressure, $n$ is the number of moles, $V$ is the volume, $R$ is the gas constant, $T$ is the temperature, and $a$ and $b$ are the van der Waals constants.

If 1 mole of a non-ideal gas, initially at 325 K and occupying 5.0 L, is allowed to expand isobarically to twice the original volume, what is the work done by the gas?

Note:

  • $a=1.355\frac{{\text{L}}^{2}\text{atm}}{{\text{mol}}^{2}}$
  • $b=3.201\times {10}^{-2}\frac{\text{L}}{\text{mol}}$
  • $R=0.0821\frac{\text{L}\times \text{atm}}{\text{mole}\times \text{K}}$
  • $1\text{ L atm}=101.325\text{ J}$
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