Q. 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, $\theta$ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is
A) $\lbrack ML^{5}T^{- 2}\rbrack$
B) $\lbrack M^{- 1}L^{5}T^{- 2}\rbrack$
C) $\lbrack ML^{- 1}T^{- 2}\rbrack$
D) $\lbrack ML^{- 5}T^{- 2}\rbrack$
Explanation
By the principle of dimensional homogenity $\lbrack P\rbrack = \left\lbrack \frac{a}{V^{2}} \right\rbrack \Rightarrow \lbrack a\rbrack = \lbrack P\rbrack \times \left\lbrack V^{2} \right\rbrack = \left\lbrack ML^{- 1}T^{- 2} \right\rbrack\lbrack L^{6}\rbrack$ $= \lbrack ML^{5}T^{- 2}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.