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' ?

If the equation of state of a gas is expressed as (P + a/(V^2)) (V - b

1.	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' ?
Answer» Solution :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 `therefore (a)/((M^(0)L^(3)T^(0))^(2))= M^(1)L^(-1) T^(-2)` `rArr (a)/(M^(0)L^(6)T^(0))= M^(1)L^(-1) T^(-2)` `therefore a= M^(1) L^(5)T^(-2)` Similarly, b will have same dimensions as volume `V-b=` volume `therefore b= M^(0) L^(3) T^(0)`