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

(1) $\left[M{L}^{5}{T}^{-2}\right]$

(2) $\left[{M}^{-1}{L}^{5}{T}^{-2}\right]$

(3) $\left[M{L}^{-1}{T}^{-2}\right]$

(4) $\left[M{L}^{-5}{T}^{-2}\right]$

Concept Videos :-

#1 | Basic Concepts & Examples
#2 | Dimensional Analysis : Remaining

Concept Questions :-

Dimensions

(1) By the principle of dimensional homogenity

$\left[P\right]=\left[\frac{a}{{V}^{2}}\right]⇒\left[a\right]=\left[P\right]×\left[{V}^{2}\right]=\left[M{L}^{-1}{T}^{-2}\right]\text{\hspace{0.17em}}\left[{L}^{6}\right]$

= $\left[M{L}^{5}{T}^{-2}\right]$

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