Question

In vander walls equation $(P+\frac{a}{V^2})(V-nb)=RT$ , the ratio of dimensions of $a$ and $b$ is,

• A. $\left[M{L}^2{T}^3\right]$
• B. $\left[M{L}^1{T}^2\right]$
• C. $\left[M{L}^2{T}^{-2}\right]$
• D. None of the above

Answer 1

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

Since it follows the equation of state.
Dimension of $\frac{a}{V^2}$will be that of pressure . Therefore dimension of $a$ will be dimension of $P{V}^2$=$\left[M{L}^5{T}^{-2}\right]$
Dimension of b will be equivalent to that of volume V =$\left[L^3\right]$
Ratio of their dimensions $\frac{\left[M{L}^5{T}^{-}2\right]}{\left[L^3\right]}=\left[M{L}^2{T}^{-2}\right]$