Q. The dimensional formula of universal gas constant is
A) $\left\lbrack {ML}^{2}T^{- 2}\theta^{- 1} \right\rbrack$
B) $\left\lbrack M^{2}{LT}^{- 2}\theta \right\rbrack$
C) $\left\lbrack {ML}^{3}T^{- 1}\theta^{- 1} \right\rbrack$
D) None of these
Explanation
Using the relation $R = \frac{pV}{\theta}$ Dimensions of gas constant $R$ $\ \ \ \ = \frac{\begin{array}{r} dimensions\ of\ pressure\ \times dimensions\ of\ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ volume \end{array}}{dimension\ of\ temperature}$ $\ \ \ \ = \frac{\left\lbrack ML^{- 1}T^{- 2} \right\rbrack\left\lbrack L^{3} \right\rbrack}{\theta}$ $\ \ \ = \left\lbrack ML^{2}T^{- 2}\theta^{- 1} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.