Heat and Thermodynamics

13.11 Equilibrium State According To the Three Statistics

The equilibrium state is obtained from the conditions

 

δS = 0, δN = Σδn_t = 0, δU = Σ∈t δn_t = 0     (13.43)

 

Using δS = 0 and remembering that a_t does not vary, we deduce from Eqs 13.39 to 13.42 that

 

 

and

 

 

Using the method of undetermined multipliers, we get from Eqs 13.43 and 13.44

 

 

or

 

 

Equation 13.46 represents the distribution law in Maxwell–Boltzmann statistics. ...