Physics

The equation of the state of some gases can be expressed as $$(P + \dfrac{a}{V^2} = \dfrac{R\theta}{V})$$, where P is the pressure. V the volume, $$\theta$$ the absolute temperature and a and b are constant. The dimensional formula of a is  


ANSWER

$$[ML^5T^{-2}]$$


SOLUTION
Dimensional formula of Pressure is $$[M^{1} L^{-1} T^{-2}]$$
Dimensional formula of Volume is $$[M^{0} L^{3} T^{0}]$$

From the given equation:
$$P+\dfrac{a}{V^2}=\dfrac{R\theta}{V}$$

Dimensional formula of $$\dfrac{a}{V^{2}}$$ is same as pressure.
$$\dfrac{a}{L^6}=[M^1L^{-1}T^{-2}]$$

Therefore dimensional formula of a is $$[M^{1} L^{5} T^{-2}]$$
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