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

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