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

The equation fo state of a gas is given by (P+(a)/(V^(3)))(V-b^(2))=c

1.	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
Answer» `[ML^(8)T^(-2)] and [L^(3//2)]` `[ML^(5)T^(-2)] and [L^(3)]` `[ML^(5)T^(-2)] and [L^(6)]` `[ML^(6)T^(-2)] and [L^(3//2)]` Solution :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)]`