Consider a two-state system at thermal equilibrium having energies 0 and 2kBT for which the degeneracies are 1 and 2, respectively

Q. Consider a two-state system at thermal equilibrium having energies 0 and 2kBT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is ______.  (Round off to two decimal places)

(kB is the Boltzmann constant)

Solution:

General formula is q = Ʃ gi e-Ei / KT,

For a two state system , 

q = Ʃ gi e^{-Ei / KT} 

⇒ q =  g1 e-E1 / KT +  g2 e-E2 / KT 

⇒  q =  1 e0 / KT +  2 e-2 / KT 

⇒ q =  1 +  2 e-2 

⇒ q = 1 + 0.27 

⇒  q = 1.27.