Energy cost lower bound for seawater desalination

[richard1941]

I was interested in the value function, (2p-1)ln((p-1)/p). It is of interest in the thermodynamics of material purification. Does anybody know where I can learn more about the statistical-mechanics underpinnings of this function?

Generally, I want to learn more about entropy. There are three flavors of entropy: (1) related to the concentration of heat in thermodynamics, (2) related to the concentration of probability in information theory (and possibly in quantum mechanics, too), and (3) the concentration of materials and the purity thereof.

The third kind of entropy is mostly encountered in the separation of fissile uranium from fertile uranium, but my interest is in the separaton of pure water from sea water. Particularly, is there a lower bound to the energy cost of desalination of sea water? If so, how close are the present RO and flash distillation systems to that lower bound?

Guidance to elementary texts is sought. I last studied thermo in 1963, so have mercy!

 

[Greg Bernhardt]

Value theory is a branch of mathematical logic that studies the relationship between the values of mathematical objects and the objects themselves. It has applications in mathematical analysis, functional analysis, number theory, algebra, algebraic geometry, representation theory, set theory, combinatorics, and other areas. Value (or valuation) theory arose in the study of lattices in order to gain insight into the fundamental properties of lattices. As its name suggests, it studies how the values of mathematical objects are related to the objects themselves.