Question

At high pressure van der Waals equation becomes :

• A. $PV=RT$
• B. $PV=RT+\frac{a}{V}$
• C. $PV=RT-\frac{a}{V}$
• D. $PV=RT+Pb$

Answer 1

Answer: (D)

$PV=RT+Pb$

Answer 2

van der Waals equation of state is
$\left[ P+\frac{a}{{{V}^{2}}} \right]\,(V-b)=RT$
when pressure is high, value of $V$ will be very small and the quantity $\frac{a}{V^{2}}$ becomes small and can be neglected in comparison to $P$.
Thus, the above equation becomes $P(V-b)=RT$
$PV-Pb=RT$
$PV=RT+Pb$
The product $PV$ becomes greater that $RT$ by an amount equal to $P-b$.
This explain that curves start rising at high pressure.