The dimensional formula of the universal gas | vedclass

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Question

(A) The ideal gas equation is given by $PV = nRT$,where $R$ is the universal gas constant.Rearranging for $R$,we get $R = \frac{PV}{nT}$.The dimension

Vedclass · Accepted Answer

$[M L^2 T^{-2} 	heta^{-1}]$

Vedclass · Answer

(A) The ideal gas equation is given by $PV = nRT$,where $R$ is the universal gas constant.Rearranging for $R$,we get $R = \frac{PV}{nT}$.The dimensions of pressure $P$ are $[M L^{-1} T^{-2}]$.The dimensions of volume $V$ are $[L^3]$.The dimensions of amount of substance $n$ are $[mol]$ (or often represented as dimensionless in basic dimensional analysis if $	heta$ represents temperature).The dimensions of temperature $T$ are $[	heta]$.Substituting these into the formula: $R = \frac{[M L^{-1} T^{-2}] 	imes [L^3]}{[	heta]} = [M L^2 T^{-2} 	heta^{-1}]$.Thus,the correct option is $A$.

The dimensional formula of the universal gas constant is:

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