24) There are several ways of approaching this problem. The first thing to realize is that the total free energy change for going from sea water to pure water will just be equal to the difference in the chemical potentials between the two. Obviously, the chemical potential of water in the sea water is lower (because it has stuff dissolved in it) and therefore pure water is not going to be generated spontaneously. This applies to all methods since it just deals with the beginning and end states of the system. Method a) and b) have the problem that they both involve transferring heat from a hot source to a cold sink. This will always be irreversible and lost energy will be above and beyond the actually energy required to "unmix" the salt from the water. This leaves b) which is simply a matter of putting enough pressure on the salty water to overcome the osmotic force in the reverse direction. This can be performed almost reversibly and is thus usually the method of choice. Try playing with some calculations of work either using a hot and cold bath for heating and condensation (or the reverse for freezing and melting). You will find that you can make it pretty efficient if the temperatures of the baths are close together. However, it will also be very slow since things vapor will not be formed and condensed very rapidly if the temperatures are close together. Also try calculating the pressure and work per liter that would be required assuming a roughly 150 mM NaCl concentration for sea water. Here the losses are not so great because the pressure does not, in principle, need to be very much higher than the osmotic pressure to get the water to flow fairly rapidly.