The equation of state for some gases is given | 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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$[ML^5T^{-2}]$

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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 $(P + \frac{a}{V^2})$,the dimensions of $\frac{a}{V^2}$ must be equal to the dimensions of pressure $P$.So,$[\frac{a}{V^2}] = [P]$.$[a] = [P] 	imes [V^2]$.The dimensions of pressure $P$ are $[ML^{-1}T^{-2}]$ and the dimensions of volume $V$ are $[L^3]$.Therefore,$[a] = [ML^{-1}T^{-2}] 	imes [L^3]^2$.$[a] = [ML^{-1}T^{-2}] 	imes [L^6]$.$[a] = [ML^5T^{-2}]$.

The equation of state for some gases is given by $(P + \frac{a}{V^2})(V - b) = RT$,where $P$ is pressure,$V$ is volume,$T$ is absolute temperature,and $a, b, R$ are constants. What are the dimensions of '$a$'?

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