Units & Dimensions

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42 of 149

Question 42 of 149

The equation for real gas is given by (P+aV2)(V−b)=RT\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}, where P,V,T\mathrm{P}, \mathrm{V}, \mathrm{T} and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab−2\mathrm{ab}^{-2} is equivalent to that of :

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Answer: (D) Energy density

[P+aV2](V−b)=RT∴[a]=[P][V2]=ML−1 T−2 L6=ML5 T−2[ b]=[V]=L3[ab−2]=ML5 T−2 L−6=ML−1 T−2\begin{aligned} & {\left[\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right](\mathrm{V}-\mathrm{b})=\mathrm{RT}} \\ & \therefore[\mathrm{a}]=[\mathrm{P}]\left[\mathrm{V}^2\right]=\mathrm{ML}^{-1} \mathrm{~T}^{-2} \mathrm{~L}^6=\mathrm{ML}^5 \mathrm{~T}^{-2} \\ & {[\mathrm{~b}]=[\mathrm{V}]=\mathrm{L}^3} \\ & {\left[\mathrm{ab}^{-2}\right]=\mathrm{ML}^5 \mathrm{~T}^{-2} \mathrm{~L}^{-6}=\mathrm{ML}^{-1} \mathrm{~T}^{-2}}\end{aligned}
Dimension of energy density.

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