Question

Consider a system composed of a very large number (N >>1) of indistinguishable atoms,
each of which has only two energy levels 0 and . In thermodynamic equilibrium, there
are n particles each with energy  and the total energy of the system is E. (10 points)
a) Write and equation for the number of microstates  in terms of N, E, and .
b) Use the Stirling approximation to write an equation for the entropy S.
E 1 and N E 1
 
      
 

Answer 1

So n particle are in energy level 0 and n particle with (symbol is missing so i assumed this)

so total energy

so

so number of microstate

2) so entopy

now using sterling approximation

so,

so we get