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An equation of a gas is given as (P+(a)/...

An equation of a gas is given as `(P+(a)/(V^(2))=(bT)/(V)`, where P = pressure, V = volume and T= absolute temperature of the gas and a and b are constants. What is the dimensional formula for a?

A

`[M^(-1)L^(5)T^(2)]`

B

`[M L^(5)T^(-2)]`

C

`[M L^(-5)T^(-1)]`

D

`[M L^(5) T]`

Text Solution

Verified by Experts

The correct Answer is:
b
From the principle of homogeneity of dimensions, all terms in a physical equation must have the same dimensions.
`therefore` Dimensions of P = Dimensions of `((a)/(V^(2)))`
`therefore [a]=[PV^(2)]`
`=[(F)/(A)xxV^(2)]=[(M^(1)L^(1)T^(-2))/(L^(2))xx(L^(3))^(2)]`
`therefore [a]=[M^(1)L^(5)T^(-2)]`
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