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**The "T dS" equations and Sackur-Tetrode equation**

## Homework Statement

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

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 (?)