A certain gas obeys
Question:

A certain gas obeys $P\left(V_{m}-b\right)=R T$. The value of $\left(\frac{\partial Z}{\partial P}\right)_{T}$ is $\frac{x b}{R T}$. The value of $x$ is

Solution:

(1)

$P(v-b)=R T$

$P V-P b=R T$

$\frac{P V}{R T}-\frac{P b}{R T}=1$

$Z=1+\frac{P V}{R T}$

$\frac{d z}{d p}=0+\frac{b}{R T}$

$\Rightarrow \frac{b}{R T}=\frac{x b}{R T}$

$x=1$