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  4. The van der Waals equation for one mole of a real gas at low pressure is

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Q. The van der Waals equation for one mole of a real gas at low pressure is

Solution:

$\left(P+\frac{a}{V^{2}}\right)\left(V-b\right)=RT$
At low $P, V$ is large
$V-b \approx V$
$\left(P+\frac{a}{V^{2}}\right)\left(V\right)=RT$
$\Rightarrow PV+\frac{a}{V}=RT$
$PV=RT-\frac{a}{V}$