What Phases are Present at Equilibrium in a Water and Ice Mixture?

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The discussion centers on the thermal dynamics of a water and ice mixture in an insulated container. The heat absorbed by ice to reach its melting point is 400 J, and the total heat required for complete melting is 2100 J. The water releases 2400 J when cooled to freezing and 5200 J when fully frozen. At equilibrium, both ice and water are present, as the heat released by the water (2400 J) is sufficient to melt some ice but not all, resulting in a mixture of phases.

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Please help/confirm.

You are mixing water with ice in an insulated container. The following are given:

*the amount of heat absorbed by the ice if heated to its melting point: 400 \rm J,
*the amount of heat absorbed by the ice if it all melts (which includes the heat needed to bring the ice to its melting point): 2100 \rm J,
*the amount of heat given off by the water if cooled to its freezing point: 2400 \rm J, and
*the amount of heat given off by the water if it all freezes: 5200 \rm J.

Based on this information, at equilibrium, which phases are present?

-water only
-ice only
-ice and water

I know that the sum of heat released/absorbed in a system is equal to zero, but I'm not sure how to approach it in this problem.

I thought that the total heat absorbed when ice completely melts is 2100 (which is stated above), so the heat released by water must be equal to this. So water does not freeze and ice melts. This means that water is only present. Is this right?

Thanks.
 
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The ice is initially colder than freezing. Some heat is needed to bring it up to melting temperature.
 
So the energy released by water is used to heat the ice to melting point. Does that mean that 2500J is used by water to heat the ice? Does that leave 5100J left for energy to be released by water, but since it has to be equal to the heat absorbed, 5000J is "released" by water. So is equailibrium results in both ice and water being present?
 

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