# Interesting problem (not homework)

1. May 10, 2010

### ideasrule

Suppose I put 1 kg of -10-degree ice in a 1 m^3 vacuum chamber. How much heat do I have to add to turn all of the ice into vapor at 100 degrees Celsius?

This seems like a ridiculously simple problem, but I realized I've no idea how to solve it. First of all, ice sublimates in a vacuum, which complicates the problem a lot. Then there's the problem that when the water boils, the newly created gas has to do work against the existing pressure to expand. Any ideas?

2. May 10, 2010

### D H

Staff Emeritus
You can't. Think about what the pressure would be for 1 kg of water vapor occupying 1 cubic meter at 100 C. Then look at where that spot is on a water phase diagram.

3. May 10, 2010

### ideasrule

Right, stupid me. What if there was 0.6 kg of ice? That would make the water vapor have almost exactly 1 atmosphere of pressure.

4. May 10, 2010

### D H

Staff Emeritus
0.58835 grams would be better.

WIth this amount of water, this means the water vapor is not going to be an ideal gas. On the plus side, you can make it so the water vapor takes a jaunt along right along the gas edge of the phase diagram.