Question

In the equation $\left(P+\frac{a}{V^2}\right)(V-b)=RT,$ where P = pressure, V= volume, a and b are constants, the dimensions of a are:

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

Answer 1

Answer: (C)

According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be same.
We have given
$\left(p+\frac{a}{V^2}\right)(V-b)=RT$
According to principle of homogeneity,
$[P]=\left[\frac{a}{V^2}\right]$
or $[a]=[P]\left[V^2\right]$
or $[a]=\left[M{L}^{-1}{T}^{-2}\right]\left[L^6\right]$
$\therefore [a]=\left[M{L}^5{T}^{-2}\right]$
Note: The physical quantities separated by the symbols $+,-,=,>,<$ etc., have the same dimensions.