In Vander Waal's equation (P+a/V2)(V-b)=RT . . .

Question : In Vander Waal's equation (P+a/V²)(V-b)=RT. Here P is pressure, V is volume, T is temperature and R is gas constant. What are the dimensions of a and b.

Doubt by Rohan

Solution : 

(P+a/V²)(V-b)=RT

As per the principle of homogeneity

Dimension of 'P' = Dimension of 'a/V²'

[ML^-1T^-2]=a/[L³]²

[ML^-1T^-2]=a/[L⁶]

[ML^-1T^-2][L⁶]=a
[ML⁵T^-2]=a

a = [ML⁵T^-2]

Dimension of V  = Dimension of b

[L³]=b
b=[M⁰L³T⁰]

Hence, the dimensions of 'a' and 'b' are [ML⁵T^-2] and [M⁰L³T⁰] respectively.