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Question

The equation of state of some gases can be expressed as $$\displaystyle \left(P + \frac {a}{V^{2}} \right) \displaystyle (V -b ) = RT $$, where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the absolute temperature , and $$a$$, $$b$$ and $$R$$ are constants. The dimensions of '$$a$$' are


A
[ML5T2]
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B
[ML1T2]
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C
[L3]
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D
[L6]
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Solution

The correct option is B $$ [ML^5 T^{-2}] $$
Since $$P$$ is being added to $$\dfrac{a}{V^2}$$, thus they must have same dimensions.
Now dimension of Pressure is that of Force per unit area = $$ML^{-1}T^{-2}$$
Thus, $$ML^{-1}T^{-2}=\dfrac{|a|}{L^6}$$ or $$|a|=ML^5T^{-2}$$

Chemistry

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