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 dimension as volume V-b = volume
`:. b = M^(0)L^(3)T^(0)`