Question

In vander Waal's gas equation $(P+\frac{a}{V^2})(V-b)=RT$ . Determine the dimension of $a$ and $b$.

Answer 1

Vander Wall’s equation is given as,

$\left(P+\frac{a}{V^2}\right)\left(V-b\right)=RT$

The dimension of $a$ is given as,

$a=P{V}^2$

$=\left[M{L}^{-1}{T}^{-2}\right]{\left[L^3\right]}^2$

$=\left[M{L}^5{T}^{-2}\right]$

The dimension of $b$ is given as,

$b=V$

$=\left[L^3\right]$

Thus, the dimension of $a$ is $\left[M{L}^5{T}^{-2}\right]$ and the dimension of $b$ is $\left[L^3\right]$.