Why is the dimensional formula of Boltzmann constant and gas constant same

Asked by harshpandeykp20 | 18th Aug, 2021, 08:31: AM

Expert Answer:

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

Answered by Shiwani Sawant | 18th Aug, 2021, 05:41: PM

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