# I Freezing Engine and Specific Heats

#### sponteous

I was reading The Refrigerator and the Universe, a nice book about the history of thermodynamics, and they talked about an engine that works on the principle that water expands when it freezes. As I understand their description, it is not a reversible engine, but perhaps it could be made so. It goes like this:

1) Apply the pressure of a heavy weight to 1 kg of water at 0°C.
2) Place this inside a cooler at -1°C. The water cools down to -1°C and then freezes, rejecting a total of Q1 + L1 joules of heat to the cooler. The expanding ice lifts the weight slightly, performing work.
3) Remove the weight, so the ice is now under atmospheric pressure only.
4) Place the ice in a "warmer" at 0°C. The ice warms to 0°C, then melts, absorbing a total of Q2 + L2.

The Q's are the heat capacities of 1kg of water and ice, and the L's are the latent heats at the two temperatures.

Clearly, for this to produce work (and it seems like it would), we need Q2 + L2 > Q1 + L1. Can we assume that the latent heats are the same even though the freezing occurs at -1°C and many atmospheres pressure, while the melting occurs at 0°C and 1 atm? If so, does this constitute a conceptual argument that the specific heat of ice is greater than the specific heat of liquid water?

The choice of -1°C for the low temperature is simply for definiteness. I'm assuming the weight is whatever it needs to be to lower the freezing point to -1°C.

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