Q. The equation of state of some gases can be expressed as $\left( P + \frac{a}{V^{2}} \right)(V - b) = \ RT$. Here $P$ is the pressure, $V$ is the volume, $T\$is the absolute temperature and $a,b,R$ are constants. The dimensions of ‘$a$’ are
A) $ML^{5}T^{- 2}$
B) $ML^{- 1}\ T^{- 2}$
C) $M^{0}L^{3}T^{0}$
D) $M^{0}L^{6}T^{0}$
Explanation
By principle of dimensional homogenity $\left\lbrack \frac{a}{V^{2}} \right\rbrack = \lbrack P\rbrack$ $\therefore\ \lbrack a\rbrack = \lbrack P\rbrack\lbrack V^{2}\rbrack = \lbrack ML^{- 1}T^{- 2}\rbrack \times \left\lbrack L^{6} \right\rbrack = \lbrack ML^{5}T^{- 2}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.