We are aware of the tremendous pressures that can be developed in nature by the

ID: 2241571 • Letter: W

Question

We are aware of the tremendous pressures that can be developed in nature by the expansion of

water as it freezes into ice. This expansion can fracture rocks, erode mountains, burst piping or

initiate potholes in Cambridge streets. In the 1840's this expansion was proposed as a means to

derive a Freeze/Thaw Heat Engine.

Imagine water confined in an extremely strong rigid cylinder with a

frictionless movable piston. Upon freezing, the ice would expand and drive the piston upwards

doing work on the surroundings. The following cycle was proposed:

Initial state of system is water at 0 C.

1 to 2. Weight is moved horizontally and placed on piston lid; temperature remains constant.

2 to 3. Heat is removed from the water at 0 C and the water expands as it freezes, doing work

by displacing the weight at constant pressure.

3 to 4. The weight is moved horizontally off of the piston; temperature remains constant.

4 to 1. Heat is transferred to the ice at 0 C, which contracts upon melting to return to its initial

condition.

From the sketch of the nal state of system, it is evident that net work has been done in raising

the weight.

a) Assuming the cycle works as described, what does the First Law imply about the Q's and

W's involved? Be specic, i.e. identify Q's and W's pertaining to the individual processes

within the cycle.

b) Which statement of the Second Law does this cycle violate? Explain.

c) Given our belief that the Second Law is correct, the freeze thaw heat engine must fail in

some part of its cycle. Where does it fail? Sketch the cycle on a P-T diagram and a P-V

diagram, including the liquid-solid phase boundaries on the diagrams. Once you have gured

out how this cycle will work in real life, determine its thermodynamic eciency if all steps

are reversible.

first law

Q supplied = change in internal energy U+W done

-Qout liquid = change in U liquid + Work done on block (freezing of water)

Qin ice = change in U ice + work done (melting of ice)

Qin ice - Qout liuid = net work done

b) In the cooling of liquid the internal energy of liquid converts to work done which is agains the 2nd law

c) it will fail in the expansion part

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