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The equation of state for a real gas hav...

The equation of state for a real gas having pressure P, volume V and temperature T is expressed as
`(P+(a)/(V^(2)))(V-b)=RT`
where a, b and R are constant. What are the dimensional formula of `(a)/(b)`?

A

`[M^(2)L^(2)T^(-2)]`

B

`[M^(1)L^(1)T^(-2)]`

C

`[M^(1)L^(2)T^(-2)]`

D

`[M^(2)L^(3)T^(-1)]`

Text Solution

Verified by Experts

The correct Answer is:
c
In a dimensional equation, every term has the same dimensions as only quantities having the same dimensions can be added or subtracted.
`because` In the term (v - b), b has the dimensions of V or `L^(3)`.
Similarly dimensionally `P=(a)/(V^(2))`
`therefore a=PV^(2)`
`therefore [a]=[("Force")/("Area")xx("Area"xxL)^(2)]`
`=[Fxx"Area"xxL^(2)]`
`therefore [a]=[L^(1)M^(1)T^(-2)xxL^(2)xxL^(2)]=[L^(5)M^(1)T^(-2)]`
`therefore [(a)/(b)]=[(L^(5)M^(1)T^(-2))/(L^(3))]=[M^(1)L^(2)T^(-2)]`
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