Units & Dimensions

JEE Main level, single correct, medium

66 of 149

Question 66 of 149

The equation of state of a real gas is given by (P+aV2)(V−b)=RT\left(P+\dfrac{a}{{V}^{2}}\right)(V-b)=RT, where P,VP,V and TT are pressure, volume and temperature respectively and RR is the universal gas constant. The dimensions of ab2\dfrac{a}{{b}^{2}} is similar to that of :

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Answer: (B) PP

From the dimensional analysis, it follows that
[P]=[aV2]⇒[a]=[PV2]...(1)[P]=\left[\dfrac{a}{{V}^{2}}\right] \Rightarrow [a]=\left[{PV}^{2}\right]...\left(1\right)
And,
[V]=[b][V]=[b]
Hence,
[ab2]=[PV2][V2]=[P]\begin{matrix}\left[\dfrac{a}{{b}^{2}}\right] & = & \dfrac{\left[{PV}^{2}\right]}{\left[{V}^{2}\right]} \\ & = & [P]\end{matrix}

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