What are the dimensions of Gas constant?

What are the dimensions of Gas constant?
  1. \(\left[M L T^{-2} K^{-1}\right]\)
  2. \(\left[M^{0} L T^{-2} K^{-1}\right]\)
  3. \(\left[M L^{2} T^{-2} K^{-1} \mathrm{~mol}^{-1}\right]\)
  4. \(\left[M^{0} L^{2} T^{-2} K \right]\)

Solution

\(\begin{aligned} P V=& n R T \Rightarrow R=\frac{P V}{n T}=\frac{M L^{-1} T^{-2} \times L^{3}}{m o l \times K} \\ &=\left[M L^{2} T^{-2} K^{-1} \mathrm{~mol}^{-1}\right] \end{aligned}\) ^

Asked in: JEE Mains - Units and Dimensions - Chapter Test

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