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The T dS equations and Sackur-Tetrode equation

  • Thread starter mathman44
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  • #1
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The "T dS" equations and Sackur-Tetrode equation

Homework Statement



This is a bit of a dumb question (I hope)

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I'm having trouble with part (e).

The Attempt at a Solution



to show it for (a), dS is given, so [tex] T\times{NK_bln{\frac{V_f}{V_i}} = P\times{dV}[/tex] since dU = 0 for isothermal process. P can be written as [tex]\frac{NK_bT}{V}[/tex], but this is clearly not equal to what I got in part A... although it would be if I integrated the right side (?)
 

Answers and Replies

  • #2
LeonhardEuler
Gold Member
859
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The TdS equation has TdS on the left hand side, you have an expression for [itex]\Delta S[/itex] of a process with a macroscopic change. Do you know that
[tex]d(\ln{x})=\frac{d(\ln{x})}{dx}dx =\frac{dx}{x}[/tex]
?
 
  • #3
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Was I wrong to assume that [tex]\Delta{S} = dS[/tex]?
 
  • #4
LeonhardEuler
Gold Member
859
1


Yes, if you use Vf and Vi on the left hand side, you need to use them on the right hand side and take the limit
[tex]\lim_{V_{f}\rightarrow V_{i}}[/tex]
on both sides and show that the ratio of the left hand side to the right hand side approaches 1, but it's much easier to just use the relation I mentioned.
 

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