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The equation fo state of a gas is given ...

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

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)]`

Text Solution

Verified by Experts

The correct Answer is:
A
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)]`
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