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

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

##### 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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Single Correct Medium Published on 18th 08, 2020
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