The equation fo state of a gas is given by
`(P+(a)/(V^(3)))(V-b^(2))=cT`, where P,V,T are pressure, volume and temperature respectively, and a,b,c are constants. The dimesions of a and b are respectively

Options

A. `[ML^(8)T^(-2)] and [L^(3//2)]`
B. `[ML^(5)T^(-2)] and [L^(3)]`
C. `[ML^(5)T^(-2)] and [L^(6)]`
D. `[ML^(6)T^(-2)] and [L^(3//2)]`

Answer

A

Explanation

Given `[P+(a)/(V^(3))](V-b^(2))=cT`
Dimension of `(a)/(V^(3))`=dimension of `PV^(3)`
`[a]=[(F)/(A)V^(3)]" "(becauseP=(F)/(A))`
`=([MLT^(-2)])/([L^(2)])xx[L^(3)]^(3)=[ML^(8)T^(-2)]`
Dimensions of `b^(2)`=dimensions of V
`therefore[b]=[V]^(1//2)=[L^(3)]^(1//2)` or `[b]=[L^(3//2)]`