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
So n particle are in energy level 0 and n particle with (symbol is missing so i assumed this)
so total energy
so number of microstate
2) so entopy
now using sterling approximation
so we get
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