Thermal Physics - Partition Function

A system consists of N weakly interacting subsystems, each with two internal quantum states with energies 0 and . The internal energy for this system at absolute temperature T is equal to

A.

B.

C.

D.

E.

(GR9677 #94)

Solution:

A. FALSE. It’s not an exponential function

B. FALSE. It’s not an exponential function

C. FALSE.  as    but     as   

D. TRUE.   as    and    as  
(fits the equipartition theorem for high temperature/classical region/Maxwell-Boltzmann Statistics)

E. FALSE.   as    and    as  


Alternative Solution #1:

Partition function



with energies 0 and ,



Energy





For N subsystems,



Answer: D 



Alternative Solution #2:

We can also use



with  , as







For N subsystems,