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The vander Waal's equation for n moles o...

The vander Waal's equation for `n` moles of a real gas is `(p + (a)/(V^(2))) (V-b) = nRT` where `p` is pressure, `V` is volume, `T` is absoulte temperature, `R` is molar gas constant `a,b` and `c` are vander Wall's constants. The dimensional formula for `ab` is

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By principle of homogentiy 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^(6) T^(0)) = [M^(1) L^(-1) T^(-2)]`
`:. a = [M^(1) L^(5) T^(-2)]`
similarly, `b` will have same dimesions as volume `V-b` = volume
`:. b = [M^(o) L^(3) T^(0)]`
`:. [ab] = [M^(1) L^(5) T^(-2)] [M^(0) L^(3) T^(0)] = [M^(1) L^(8) T^(-2)]`
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