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Q & A: Entropy and volume of water vs. temperature

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Most recent answer: 02/28/2011
Q:
Does the entropy of liquid water increase or decrease when heated from 0 degrees celsius to 4 degrees celsius
- Niharika (age 18)
India
A:
The entropy of any stable material always goes up when it's heated. That turns out to be equivalent to saying that the heat capacity and temperature are always positive. Positive temperature (dU/dS)|V is required for anything in equilibrium with electromagnetic fields, since they can always gain entropy by gaining energy. Positive heat capacity is required because for negative heat capacity, the entropy S could be increased by having the material redistribute its energy in some non-uniform way.

Your question no doubt was triggered by an interesting fact. The volume of water at atmospheric pressure decreases from 0C to 4C. That's unusual, since most materials expand when heated.

So your question brings up a very important point. There's an enormous distinction between rules-of-thumb (such as the tendency of most materials to expand when heated)  and precise theorems (such as the requirement that the entropy of any stable material increase on heating).

Mike W.

(published on 02/28/2011)

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