Q. In the gas equation $\left( p + \frac{a}{V^{2}} \right)(V - b) = RT,$ the dimensions of $a$ are
A) $\left\lbrack {ML}^{3}T^{- 2} \right\rbrack$
B) $\left\lbrack M^{- 1}L^{3}T^{- 1} \right\rbrack$
C) $\left\lbrack {ML}^{5}T^{- 2} \right\rbrack$
D) $\left\lbrack M^{- 1}L^{- 5}T^{2} \right\rbrack$
Explanation
Given, $\left( p + \frac{a}{V^{2}} \right)(V - b) = RT$ According to principle of homogeneity Dimension of $\frac{a}{V^{2}} =$ dimension of $p$ Dimension of $a =$ dimension of $p \times$ dimension of $V^{2}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack ML^{- 1}T^{- 2} \right\rbrack\left\lbrack L^{3} \right\rbrack^{2} = \left\lbrack ML^{5}T^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.