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Why is the dimensional formula of Boltzmann constant and gas constant same
Asked by harshpandeykp20 | 18 Aug, 2021, 08:31: AM
Boltzmann constant = Energy/ Temperature
= Energy x (Tempertaure)-1
Dimensions of Energy = [M1 L2 T -2
Dimensions of Temperature = [K]

Thus,
Dimensions of Boltzmann constant = [M1 L2 T -2] x [K]-1  = [M1 L2 T -2 K-1

Gas constant = Pressure x Volume / (Total no.of moles x Temperature)
= Pressure x Volume x (Total no.of moles x Temperature)-1
i.e
R = PV/nT
Dimensions of Pressure = [M1 L-1-2]
Dimensions of Volume  = [L3
Dimensions of temperature = [K]
Dimensions of Gas constant = [M1 L-1 T -2] x [L3] x [K]-1  = [M1 L2 T -2 K-1

Thus, you can observe that both Boltzmann constant and Gas constant have same dimensional formula
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