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During the classic high school latent heat experiment a solid such as ice is heated from below the melting point until it is a liquid above the melting point. During this experiment the temperature rises until it reaches the melting point then remains constant for some time and once the solid is melted it continues to rise.

The question is if we stopped the experiment half way through the time of constant temperature what physical difference could we see in the material?

Another way to ask the question would be if we just had a piece of ice made up of two molecules what would the latent heat experiment temperature verses time curve look like?

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At the risk of an anticlimax halfway through the experiment, half the ice will have melted. There is no special phase of matter that is halfway between water an ice (at least not for water). You simply have one or the other.

If you look at what is going on at the atomic level you will find two processes are occurring. Water molecules are breaking off the ice crystals to join the liquid water. At the same time other water molecules will be bonding back onto the crystal from the liquid. If you have water at its melting point both these process happen at the same rate, so molecules are continually moving between being in the liquid and the solid, but the total amount of each does not change. If you or cool the mixture, you make one of these processes speed up while the other slows down, leading to respectively more liquid water or ice in the equilibrium.

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