The van der Waals' equation of state for some gases can be expressed as:$$P+aV2(V$$−$$b)=RTwhere$$ P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a, b, and R are constants.The dimensions of a areThe dimensions of constant b areWhich of the following does not have the same dimensional formula as that for RT?The dimensional representation of $$ab/RT$$ isIn the above problem, the dimensional formula for RT is same as that of

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[a]$$=PV2=FV2A=MLT$$−$$2L6L2=ML5T$$−$$2$$[b]$$=$$[V]$$=L3According$$ to given equation, $$PV+aV$$−Pb−$$abV2=RTAs$$ dimensions of all the terms on LHS must be equal to dimensions of term RT on RHS, $$a/V2$$ does not have the same dimensional formula as that of RZ.$$abV2=$$[RT]⇒$$abRT=V2=L6$$[RT]$$=$$[PV]$$=FA$$⋅$$V=ML2T$$−$$2So$$ the dimensional formula of RT is same as that of energy.

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