Question

At low pressure if $RT=2\sqrt{a.p}$, ( a is van der Waals' constant), then the volume occupied by a real gas is :

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

Answer 1

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

$\text{We know, at low pressure, Vander Waal's equation can be:}$

$(P+\frac{a}{V^2})\left(V\right)=RT$ $\Rightarrow P{V}^2-\left(RT\right)V+a=0.$

$\therefore V=\frac{RT\pm \sqrt{R^2{T}^2-4Pa}}{2P}$

$=\frac{RT\pm \sqrt{R^2{T}^2-4\times \frac{R^2}{4}}{T}^2}{2P}$

$=\frac{RT}{2P}$

$(\because RT=2\sqrt{Pa})$

$\text{Thus, volume occupied by real}gas=\frac{RT}{2P}$