van't Hoff-van der Waals osmotic pressure and energy transformers

We find the van't Hoff relations between osmotic pressure, freezing point depression, and boiling point elevation provide a clue on how, by using salt solutions, one may lower the cost of extracting power from low-grade heat sources. In particular, the ratio of 7 between the heat of evaporation and the heat of freezing of pure water suggests a chemical system that raises 7-fold the temperature difference between heat source and heat sink, while decreasing by the same factor the heat flux. Heat exchangers dominate the cost of heat engines operating upon low-grade heat. Their area for a fixed power output is inversely proportional to the available temperature differential. Herein lies the potential for a great cost reduction. We show that the simple van der Waals concept of a gas of hard elastic spheres suffices to understand the colligative properties of salt solutions, at least up to the concentration of the eutectic composition. This concept enables us to physically interpret the thermodynamic processes during the concentration of salt solutions by evaporation and during the mixing of ice and solid salt hydrates at their eutectic temperature. These are identical to the thermodynamic processes taking place during the isothermal compression and expansion of gases in pumps and in turbines.