In Vander Waal's equation left[ P + frac{a}{V | vedclass

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(A) According to the principle of homogeneity of dimensions,only physical quantities with the same dimensions can be added or subtracted.In the term $

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$M^1 L^5 T^{-2}$

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(A) According to the principle of homogeneity of dimensions,only physical quantities with the same dimensions can be added or subtracted.In the term $\left( P + \frac{a}{V^2} ight)$,the dimensions of $P$ must be equal to the dimensions of $\frac{a}{V^2}$.Therefore,$[P] = \left[ \frac{a}{V^2} ight]$.This implies $[a] = [P] 	imes [V^2]$.We know that pressure $P$ is force per unit area,so $[P] = [MLT^{-2}] / [L^2] = [ML^{-1}T^{-2}]$.Volume $V$ has dimensions $[L^3]$,so $[V^2] = [L^3]^2 = [L^6]$.Substituting these values,we get $[a] = [ML^{-1}T^{-2}] 	imes [L^6] = [ML^5T^{-2}]$.Thus,the dimensions of $a$ are $[M^1 L^5 T^{-2}]$.

In Vander Waal's equation $\left[ P + \frac{a}{V^2} \right] (V - b) = RT$,the dimensions of $a$ are

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