Learn Thermodynamics of Material Purification & Entropy for Desalination

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SUMMARY

The discussion focuses on the thermodynamics of material purification and entropy, particularly in the context of desalination. The value function discussed, (2p-1)ln((p-1)/p), is relevant to understanding the statistical mechanics behind these concepts. The conversation highlights three types of entropy: thermodynamic heat concentration, probability concentration in information theory, and material purity concentration, with a specific interest in the energy costs associated with desalinating seawater. Participants seek guidance on foundational texts to refresh their knowledge in thermodynamics and its applications in desalination technologies.

PREREQUISITES
  • Understanding of thermodynamics principles
  • Familiarity with entropy concepts in physics
  • Basic knowledge of statistical mechanics
  • Awareness of desalination technologies such as reverse osmosis (RO) and flash distillation
NEXT STEPS
  • Research the thermodynamic principles of desalination energy costs
  • Study the statistical mechanics related to the value function (2p-1)ln((p-1)/p)
  • Explore foundational texts on entropy in thermodynamics and information theory
  • Investigate current advancements in reverse osmosis and flash distillation systems
USEFUL FOR

Researchers, engineers, and students interested in thermodynamics, material purification, and the efficiency of desalination processes will benefit from this discussion.

richard1941
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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!
 
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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.