The equation of state of a real gas is given by (P + a V ^ 2 ) ( V...

From the dimensional analysis, it follows that

$[ P ] = \left[\dfrac{a}{{V}^{2}}\right] ⇒ [ a ] = \left[{PV}^{2}\right] . . . \left(1\right)$

And,

$[ V ] = [ b ]$

Hence,

$\begin{cases}\left[\dfrac{a}{{b}^{2}}\right] & = & \dfrac{\left[{PV}^{2}\right]}{\left[{V}^{2}\right]} \\ & = & [ P ]\end{cases}$