Science
Entropy and the microscopic meaning of temperature

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need help for the solution of 2 attached problems about Entropy and the microscopic meaning of temperature

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Problem 2.34. Show that during the quasi static isothermal expansion of a monatomic ideal gas, the change in entropy is related to the heat input Q by the simple formula.

In the following chapter I’ll prove that this formula is valid for any quasistatic process. Show, however, that it is not valid for the free expansion process described above.

Final Answer

attached is my answer

Problem 2.34:
During the quasistatic isothermal expansion, we have Q = −W , where Q is the heat and W is
the work done.
Integrating the ideal gas law in terms of dV , it follows that

Q = −W
Vf

Q=



Vi

NkT
dV
V

 Q = NkT ln V V f
V

i

 Q = NkT ( ln V f − ln Vi )
V 
 Q = NkT ln  f 
 Vi 

 Vf
 Vi


 , which immediately

 Vf 
Q
implies the desired equation S = because the last equation Q = NkT ln   implies that
T
 Vi 
Moreover, the Sackur-Tetrode equation implies that S = Nk ln 

V  Q...

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