A) \[ML{{\,}^{5}}{{T}^{-2}}\]
B) \[ML{{\,}^{4}}{{T}^{-1}}\]
C) \[ML{{\,}^{3}}{{T}^{-1}}\]
D) \[ML{{\,}^{5}}{{T}^{-1}}\]
Correct Answer: A
Solution :
Van der Waals equation is given by \[\left( P+\frac{a}{{{V}^{2}}} \right)(V-b)=RT\] Dimensions of a = dimensions of P x dimensions of \[{{V}^{2}}\] \[\text{=}\frac{\text{dimensions}\,\text{of}\,\text{force}}{\text{dimensions}\,\text{of}\,\text{area}}\text{ }\!\!\times\!\!\text{ dimensions}\,\text{of}\,{{V}^{2}}\] \[=\frac{ML/{{T}^{2}}}{{{L}^{2}}}\times {{L}^{6}}=M{{L}^{-1}}{{T}^{-2}}\times {{L}^{6}}\] \[=M{{L}^{5}}{{T}^{-2}}\]
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