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The Working Subject
The foundational arguments elsewhere in this bundle are real, and they are almost entirely invisible from where the subject is actually practised. A chemical engineer sizing a distillation column, a biochemist calculating whether a reaction proceeds, a designer improving a refrigeration cycle: none of them needs a position on whether entropy is objective, or whether thermodynamics reduces to statistical mechanics. This section is about that trunk, which is where most people meet the subject and where nearly all of its use lies.
Chemical thermodynamics
The largest branch by usage, and the one Gibbs built. Its central quantities are the free energies — Gibbs free energy at constant temperature and pressure, Helmholtz free energy at constant temperature and volume — which answer the question a chemist actually has: will this reaction go, and how far? A negative change in Gibbs free energy means the reaction proceeds spontaneously; the magnitude fixes the equilibrium constant.
The apparatus built on this is substantial: chemical potential, which governs how matter distributes itself between phases and reactions; phase equilibria and the phase rule; activity coefficients for real rather than ideal mixtures; and the temperature dependence that makes reaction engineering possible. It is the reason thermodynamics appears in every chemistry degree, and its results are not in dispute.
Engineering
This is where the subject began. Sadi Carnot’s Reflections on the Motive Power of Fire (1824) asked how much work could be obtained from a heat engine, and answered with a limit depending only on the two temperatures between which it operates — a result derived before the first law was formulated, and before anyone knew what heat was.
The practical descendants are the cycles: Carnot as the ideal limit, Rankine for steam plant, Otto and Diesel for internal combustion, Brayton for gas turbines, and the vapour-compression cycle that makes refrigeration and heat pumps work. Exergy analysis — accounting for the fraction of energy in a stream that is actually available to do work — is the modern form of the same question Carnot asked, and is the standard tool for finding where a plant wastes its capacity.
The historical direction runs opposite to the usual picture of physics: the theory came out of the machines rather than the machines out of the theory.
Bioenergetics
Living things are thermodynamic systems, and the accounting works. Chemiosmosis — Peter Mitchell’s proposal, initially resisted and later awarded the Nobel Prize in Chemistry in 1978 — established that cells store energy as an electrochemical gradient across a membrane and use its discharge to synthesise ATP. Metabolic pathways are analysed through free energy changes in exactly the chemical-thermodynamic terms above, and the coupling of unfavourable reactions to favourable ones is the mechanism by which cells do work against a gradient.
A separate and much less settled strand shares the topic name: attempts to characterise living organisation itself thermodynamically — maximum entropy production principles, dissipative-structure accounts of the origin and maintenance of life. These are research programmes with open questions, not settled results, and the difference in confidence between them and the metabolic accounting above is large enough that running them together would misrepresent both.
See also: Thermodynamics · Away from equilibrium · Gibbs · Autopoiesis