Question

At high pressures, the compressibility factor $z$ is equal to

• A. unity
• B. $1-\frac{Pb}{RT}$
• C. $1+\frac{Pb}{RT}$
• D. zero

Answer 1

Answer: (C)

$P+\frac{a}{V^2}(V-d)=RT$
At high pressure $b$ can not be neglected in comparison to $V$.
Further though $V$ becomes small, $\frac{a}{V^2}$
is large but as $P$ is very high, $\frac{a}{V^2}$.
Can be neglected in comparison to $P$. Hence,
$P(V-d)=RT$ or $PV=RT+Pb$
or $\frac{PV}{RT}=1+\frac{Pb}{RT}$
i.e, $z=1+\frac{Pb}{RT}$