The equation for a real gas is given by (P + | vedclass

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(D) The given equation is $(P + \frac{a}{V^2})(V - b) = RT$. According to the principle of homogeneity of dimensions,dimensions of terms added or subt

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Energy density

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(D) The given equation is $(P + \frac{a}{V^2})(V - b) = RT$. According to the principle of homogeneity of dimensions,dimensions of terms added or subtracted must be the same. Therefore,$[P] = [\frac{a}{V^2}] \implies [a] = [P][V^2]$. Since $[P] = ML^{-1}T^{-2}$ and $[V] = L^3$,we have $[a] = (ML^{-1}T^{-2})(L^6) = ML^5T^{-2}$. Also,$[b] = [V] = L^3$. Now,the dimension of $ab^{-2}$ is $[a][b]^{-2} = (ML^5T^{-2})(L^3)^{-2} = (ML^5T^{-2})(L^{-6}) = ML^{-1}T^{-2}$. This dimension $ML^{-1}T^{-2}$ is the same as the dimension of pressure or energy density (Energy/Volume = $ML^2T^{-2} / L^3 = ML^{-1}T^{-2}$).

The equation for a real gas is given by $(P + \frac{a}{V^2})(V - b) = RT$,where $P, V, T$ and $R$ are the pressure,volume,temperature,and gas constant,respectively. The dimension of $ab^{-2}$ is equivalent to that of

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