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Re: Entropy Change Problem

Regarding Don P.'s calculation:
...
Unfortunately, ln(1+x) - x is < zero for all x > 0, so I have calculated
that dS_net is < 0 rather than the answer I wanted (> 0)

Would appreciate your help in finding my error or errors.

It seems you made no errors in your calculation. The problem is in
you wanting dS_net to be positive. It really *should* be negative.
This is because the process you described is an impossible non-
spontaneous one. What you have shown is that it is not possible for
liquid water to isothermally freeze while releasing its latent heat
to *only* a surrounding gas whose initial temperature was at the
freezing point.

If you placed a mass of liquid water in thermal contact with only a
surrounding gas and insulated the combined water/gas system from the
rest of the universe after first requiring that the initial
temperature of both the water and the gas was at the freezing point
of the water, then you would find that the water *doesn't* freeze.
It *stays* liquid.

David Bowman