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Water expands when it heats up. If you heat water in a container that prevents it from expanding, will its temperature top out -- maybe around the boiling point?

And if not, will it still turn to gas without room to expand?

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Because cv < cp the temperature will rise more for the same amount of heat added. "Turning to gas", yes, of course, You have to heat above critical temperature. But that "gas" is very strange, called supercritical water, it has very exotic properties, ranging from liquid-like to real gas without a transition in between. –  Georg Oct 26 '11 at 9:34
    
@Georg: I think your comment is actually an answer. –  C.R. Oct 26 '11 at 9:51

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No, its temperature will not stop rising. Substances have both a temperature, and a density. Remember in chemistry you had two different heat capacities, constant pressure, and constant volume. The water will still heat up, although the heat capacity is the constant volume heat capacity. At some temperature, it becomes a gas, with the same density as it started with.

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In every day use of physics, you are talking of a pressure cooker situation: a strong container and heat applied. The pressure cooker has a valve that lets off steam so as to stop the temperature at a point, higher than the boiling point of water at normal temperatures and pressures. That is the whole point of it, to cook at higher temperatures faster.

Study the phases of water in this article.

When you apply heat to a closed container with water, you change its phase into steam and mixed, raising the pressure. In the end all the energy goes to heat because there is no other outlet, and energy is conserved.

In the first plot you see that when the pressure rises, temperature rises, and even though it is a many valued function, i.e. the physical path may take different values depending on the initial conditions, still the answer is that the temperature will keep on rising until the container bursts from the pressure build up.

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The question was about a container "preventing expansion of the water". This means a (hypothetical) container with zero volume expansion and fantastic strength. –  Georg Oct 27 '11 at 9:43
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@Georg, maybe you are unfamiliar with kitchen utensils, but that is what a pressure cooker is: a strong container so that pressure can build up to increase the cooking temperature. The only difference with the question is that the pressure cooker has an escape valve so that steam leaves and the temperature does not go higher than that specified for the cooking needs. He could do his experiment with a pressure cooker where he soldered the valve. –  anna v Oct 27 '11 at 9:50
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I'm well aware of Denise Papins pots!. I preseve two of them now more than 50 years old. Your problem seems to be, that the question is about enclosing the water in a container without free space thus "preventing expansion of it"! –  Georg Oct 27 '11 at 9:58
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If You want to rupture the gasket in the lid, go on! This gasket is the ultimate security valve in pressure cookers. This: ""water does not expand much with heat until it reaches the steam point"" is plain nonsense. All this thread is about the small expansion of liquids, which will rupture any container You might have access to. –  Georg Oct 27 '11 at 15:04
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Water has an anomaly close to freezing point, starting from 20 °C upward the dilation is 10 exp-3 as for all liquids. Volume expansion of steel is 30 * 10 exp-5 . After this excurse to the normative power of the factual, You can start to calculate. –  Georg Oct 27 '11 at 17:12

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