Question

The dimensional formula of constant a in van der Waals gas equation $\left(p+\frac{a}{V^{2}}\right)(V-b)=R T$ is :

• A. $\left[M L^{3} T^{-2}\right]$
• B. $\left[M L^{5} T^{-2}\right]$
• C. $\left[M L^{2} T^{-1}\right]$
• D. $\left[M L^{-2} T^{5}\right]$

Answer 1

Answer: (B)

Pressure $P$ and $\frac{a}{V^{2}}(V=$ volume) must have same dimensions
$\therefore $ dimensions of $[ P ]=$ dimensions of $\left[\frac{a}{V^{2}}\right]$
$\Rightarrow $ dimensions of $[a] =$ dimensions of $\left[P V^{2}\right] $
$=\left[M L^{-1} T^{-2}\right] \times\left[\left(L^{3}\right)^{2}\right]$
$=\left[M L^{5} T^{-2}\right] $