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

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

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(A) According to the principle of dimensional homogeneity,only physical quantities with the same dimensions can be added or subtracted.In the given equation $\left( {P + \frac{a}{{{V^2}}}} ight)\,(V - b) = RT$,the term $\frac{a}{{{V^2}}}$ is added to pressure $P$.Therefore,the dimensions of $\frac{a}{{{V^2}}}$ must be equal to the dimensions of pressure $P$.$[\frac{a}{{{V^2}}}] = [P]$$[a] = [P] 	imes [V^2]$We know that the dimensions of pressure $P$ are $[M{L^{ - 1}}{T^{ - 2}}]$ and the dimensions of volume $V$ are $[L^3]$.So,$[a] = [M{L^{ - 1}}{T^{ - 2}}] 	imes [L^3]^2$$[a] = [M{L^{ - 1}}{T^{ - 2}}] 	imes [L^6]$$[a] = [M{L^5}{T^{ - 2}}]$

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure,$V$ is the volume,$T$ is the absolute temperature and $a, b, R$ are constants. The dimensions of $a$ are

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