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If the equation of state of a gas is exp...

If the equation of state of a gas is expressed as `(P + a/(V^2)) (V - b) = RT` where P is the pressure, V is the volume and T the absolute temperature and a, b , R are constants, then find the dimensions of 'a' and 'b' ?

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By principle of homogeneity of dimensions P can added to P only. It means `(a)/(V^2)` also gives pressure.
Dimension formulae for pressure `(P) = M^(1) L^(-1) T^(-2)`
and Volume (V) `=M^(0) L^(3) T^(0)`.
Since `(a)/(V^2)=` pressure
`therefore (a)/( (M^(0) L^(3) T^(0) )^(2))= M^(1) L^(-1) T^(-2) rArr - (a)/( M^(0) L^(6) T^(0) ) = M^(1) L^(-1) T^(-2)`
`therefore a= M^(1) L^(5) T^(-2)`, Similarly, b will have same dimensions as volume `V-b=` volume
`therefore b= M^(0) L^(3) T^(0)`
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