Question

At low pressures, the van der Waals equation is written as $[P+\frac{a}{V^2}]V=RT$. The compressiblity factor of the gas is:

• A. $[1-\frac{a}{V}]$
• B. $[1-\frac{a}{TV}]$
• C. $[1-\frac{a}{RTV}]$
• D. $[1-\frac{RT}{aV}]$

Answer 1

The correct option is C $[1-\frac{a}{RTV}]$

Solution:- (C) $[1-\frac{a}{RTV}]$

Given that at low pressure, van der Waals equation is-

$[P+\frac{a}{V^2}]V=RT$

$\Rightarrow PV+\frac{a}{V}=RT$

$\Rightarrow \frac{PV}{RT}+\frac{a}{RTV}=1$

$\Rightarrow \frac{PV}{RT}=1-\frac{a}{RTV}$

$\Rightarrow Z=1-\frac{a}{RTV}(\because Z=\frac{PV}{RT})$

Hence the compressiblity factor of the gas is $[1-\frac{a}{RTV}]$.