Some water at 0^o C is placed in large insulated encloser. What fraction of water will ultimately freeze?

The water vapor is pumped out continuously .The latent heat of vaporization is seven times the latent heat of fusion.

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For every mole of ice that is formed the heat given up can produce 1/7 moles of vapor. As the vapor is continuously pumped out the system loses the heat produced by freezing the water. The liquid will get colder and colder and eventually there will be nothing left but ice in the container. However some of the water will be lost as vapor that has been pumped out of the container.

Suppose we have N moles of water to start with. If we make n moles of ice then N-n-n/7 moles of water will be left. Eventually there will no moles of water left and the process will stop. This means that

N-n-n/7=0 of that n=7/8N. Only 7/8 of the original water will be left all in the form of ice.

This is the same thing that happens to ponds in winter. As the water freezes it produces vapor which can be swept away by winds. More freezes, more vapor is lost, and eventually the whole pond freezes. This is called evaporative cooling.

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