Math 2.0

Classical thermodynamics, heat transfer Definition

Finite-time thermodynamics

Builds on Thermodynamic cycleReversible processIrreversible processHeat engine

Definition

Finite-time thermodynamics is the study of thermodynamic processes and cycles under these conditions.

  1. Each process, or each cycle, has a finite duration.
  2. Transport laws give the rates of heat and mass transfer in terms of differences of intensive variables, such as q=κ(T1−T2)q = \kappa (T_1 - T_2) for heat.
  3. A performance measure, such as power, efficiency at given power or entropy production, is optimised over the admissible processes.

A model in this theory is endoreversible if the system is reversible inside and all irreversible effects occur in its coupling to the surroundings.

Remarks

Example: a heat engine that takes heat from a reservoir at ThT_h through a conductance κh\kappa_h and runs a Carnot cycle inside between T1<ThT_1 < T_h and T2T_2 is an endoreversible model. Its power is a function of T1T_1 and T2T_2, and optimising it is a problem of finite-time thermodynamics. Non-example: the study of a Carnot cycle in the quasistatic limit, with zero temperature gaps, fails clause 1, because a quasistatic process takes infinite time. The terms endoreversible thermodynamics and finite-time thermodynamics are often used for the same body of work.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

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Heat engine, concept, no evidence levelHeat engineconceptIrreversible process, concept, no evidence levelIrreversible processconceptReversible process, concept, no evidence levelReversible processconceptThermodynamic cycle, concept, no evidence levelThermodynamic cycleconceptFinite-time thermodynamics, definition, no evidence levelFinite-time thermodyn…definition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Heat engine concept
  2. Irreversible process concept
  3. Reversible process concept
  4. Thermodynamic cycle concept
  5. Finite-time thermodynamics definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Endoreversible_thermodynamics
About this page
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WritingW0 stub
MSC80A10, 80M50
DefinesFinite-time thermodynamics
UsesThermodynamic cycle, Reversible process, Irreversible process, Heat engine
Changed3 November 2026

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