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What is the unit of 'a' in terms of fund...

What is the unit of 'a' in terms of fundamental units in Van der waal's equation
`(P+(a)/(V^(2)))(V-b)=RT`?

A

`kgm^(5)//s^(2)`

B

`kgm//s`

C

`kgm^(4)s^(2)`

D

`kg^(2)m^(3)//s^(2)`

Text Solution

Verified by Experts

The correct Answer is:
a
Since the quantities having the same dimensions can be added or subtracted, the dimensions of `(a)/(V^(2))` will be the same as that of pressure.
`therefore [a]=[V^(2)][P]`
But `[V]=[L^(3)]and[P]=[(F)/(A)]=[M^(1)L^(-1)T^(-2)]`
`therefore [a]=[L^(6)][M^(1)L^(-1)T^(-2)]=[M^(1)L^(5)T^(-2)]`
`therefore` The unit of a will be kg `m^(5)//s^(2)`.
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