(P + a V ^ 2 )(V - b) = RT represents the equation of state of some...

According to the principle of dimensional homogeneity, the dimensions of each terms of a dimensional equation on both sides are the same.

So, dimension of $b$ and $V$ will be same, \left[b\right] = $\left[V\right]$

And dimension of $\dfrac{a}{{V}^{2}}$ and $P$ will be same, \left[\dfrac{a}{{V}^{2}}\right] = \left[P\right]$</p><p>From above two relations, we have \left[\dfrac{a}{{b}^{2}}\right] =$\left[P\right]$</p><p>$∴ \left[\dfrac{{b}^{2}}{a}\right] = \dfrac{1}{\left[P\right]} = {\left[M{L}^{- 1}{T}^{- 2}\right]}^{- 1}$</p><p>Thus, \left[{M}^{- 1}{L}^{1}{T}^{2}\right]$ is the dimension of compressibility.