Question

A certain gas obeys $P(V_m-b)=RT.$ The value of ${\left(\frac{\delta Z}{\delta P}\right)}_T\text{is}\frac{xb}{RT}.$ The value of $x$ is_____.
(Z: compressibility factor)

Answer 1

$P(V_m-b)=RT$
$\Rightarrow P{V}_m-Pb=RT$
$\Rightarrow \frac{P{V}_m}{RT}=1+\frac{Pb}{RT}$
$\text{Compressibility factor, Z}=\frac{P{V}_m}{RT}$
$\Rightarrow Z=1+\frac{Pb}{RT}$
${\left(\frac{\delta Z}{\delta P}\right)}_T=\frac{b}{RT}$
$\therefore \begin{array}{c}x=1\end{array}$