The equation of state of a real gas is given | vedclass

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(B) According to the principle of dimensional homogeneity,terms added or subtracted in an equation must have the same dimensions.$1$. In the term $(P

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$P$

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(B) According to the principle of dimensional homogeneity,terms added or subtracted in an equation must have the same dimensions.$1$. In the term $(P + \frac{a}{V^2})$,the dimensions of $P$ must be equal to the dimensions of $\frac{a}{V^2}$.$[P] = [\frac{a}{V^2}] \Rightarrow [a] = [P][V^2] = [P][L^6]$.$2$. In the term $(V - b)$,the dimensions of $V$ must be equal to the dimensions of $b$.$[b] = [V] = [L^3] \Rightarrow [b^2] = [V^2] = [L^6]$.$3$. Now,find the dimensions of $\frac{a}{b^2}$:$[\frac{a}{b^2}] = \frac{[P][V^2]}{[V^2]} = [P]$.Therefore,the dimensions of $\frac{a}{b^2}$ are the same as the dimensions of pressure $P$.

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

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