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]
B
[ML1T2]
C
[L3]
D
[L6]

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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