Question

The dimension of $a$ in Van der Waals equation $(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$ is

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

Answer 1

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

We know that, physical quantities having same dimension are added or subtracted together.
Therefore, dimension of $\frac{a{n}^2}{V^2}$ should be same as dimension of pressure $P$.
$\Rightarrow \left[\frac{a{n}^2}{V^2}\right]=\left[P\right]$
$\Rightarrow \left[a\right]\left[\frac{n^2}{V^2}\right]=\left[P\right]$
$\Rightarrow \left[a\right]\left[L^{-6}\right]=\left[M{L}^{-1}{T}^{-2}\right]$
$\Rightarrow \left[a\right]=\left[M{L}^5{T}^{-2}\right]$
Dimension of $a$ is $\left[M{L}^5{T}^{-2}\right]$