Question

The dimensional formula of the constant a in Vander Waal's gas equation $(P+\frac{a}{V^2})(V-b)=RT$ is

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

Answer 1

The correct option is D $\left[M{L}^5{T}^{-2}\right]$

Here the dimension of $\frac{a}{V^2}$ will be equal to pressure so $\frac{a}{{\left(L^3\right)}^2}=M{L}^{-1}{T}^{-2}$

$a=M{L}^5{T}^{-2}$