Question

At low pressure, if $RT=2\sqrt{a.P}$, then the volume occupied by a real gas is (where $a$ is the van der Waal's gas constant for pressure correction)

• A. $\frac{2RT}{P}$
• B. $\frac{2P}{RT}$
• C. $\frac{RT}{2P}$
• D. $\frac{2RT}{P}$

Answer 1

The correct option is C $\frac{RT}{2P}$

At low pressure,
$(P+\frac{a}{V^2})\times V=RT\Rightarrow P{V}^2+a=RTV\Rightarrow P{V}^2-RTV+a=0$
The volume occupied by a real gas will be
$V=\frac{RT\pm \sqrt{R^2{T}^2-4Pa}}{2P}\Rightarrow V=\frac{RT\pm \sqrt{R^2{T}^2-R^2{T}^2}}{2P}.....(\because 4aP=R^2{T}^2)\Rightarrow V=\frac{RT}{2P}$