If the equation of state of a gas is expressed as `(P + a/(V^2)) (V - b) = RT` where P is the pressure, V is the volume and T the absolute temperature and a, b , R are constants, then find the dimensions of 'a' and 'b' ?

Explanation

By principle of homogeneity of dimensions P can added to P only . It means `a/(V^2)` also gives pressure.
Dimension formulae for pressure (P) = `M^1 L^(-1) T^(-2)`
and volume `(V) = M^0 L^3 T^0`
Since `a/(V^2)` = pressure
`:. (a)/((M^0 L^3 T^0)^2) = M^1 L^(-1) T^(-2)`
`implies a/(M^0 L^6 T^0) = M^1 L^(-1) T^(-2)`
`:. a = M^1 L^5 T^(-2)`
Similarly, b will have same dimensions as volume
`V - b` = volume
`:. b = M^0 L^3 T^0`.