Question

At low pressure, if $RT=2\sqrt{a.p}$, then the volume occupied by a real gas is :

• A. $\frac{2RT}{P}$
• B. $\frac{2P}{RT}$
• C. $\frac{RT}{2P}$
• D. None of these

Answer 1

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

The van der Waal equation is

$(P+a/V_m^2)(V_m-b)=RT$

At low pressures, V is large and b is negligible in comparison with V

Therefore, the equation reduces to

$(P+a/V_m^2)\left(V_m\right)=RT$

or, $P{V}_m+a/V=RT$

$P{V}_m^2+a=RT{V}_m$

$P{V}_m^2-RT{V}_m+a=0$

$V_m=\frac{-(-RT)\pm \sqrt{(RT{)}^2-4aP}}{2P}$

$=\frac{RT\pm \sqrt{(2\sqrt{aP}{)}^2-4aP}}{2P}$

$=\frac{RT\pm \sqrt{4aP-4aP}}{2P}$

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

Hence, the correct option is $\text{C}$