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Entropy and the Entropy Principle

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Clausius generalized the mathematical expression of Carnot’s principle obtained by Kelvin, and in 1865, introduced the concept of entropy and formulated the entropy principle. With the concept of entropy and the idea of the entropy principle , a definition of heat can be given, as well as mathematical formalism on equilibrium thermodynamics was formulated for organizing empirical data of thermodynamic properties. The establishment of the entropy principle signaled the beginning of a new era—in which, thermodynamics, which had originated as a branch of engineering knowledge, separated into two distinctive streams. The new science stream was manifested in the mathematical formalism on equilibrium thermodynamics. It is noted that the entropy principle , rather than the energy principle , is the true universal principle.


  • The first Clausius theorem
  • The second Clausius theorem (Clausius’ Inequality)
  • Entropy
  • The entropy principle
  • Gibbs U-V-S surface
  • Entropy functions for ideal gases
  • Approximate entropy functions for liquids/solids
  • Definition of heat
  • Carnot vapor cycle
  • Properties of ideal gas mixtures (Gibbs’ theorem)
  • Reversible mixing of ideal gases
  • Birth of equilibrium thermodynamics

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  • DOI: 10.1007/978-3-030-05746-6_5
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  1. 1.

    The Carnot machine operates as a Carnot heat engine during some microcycles and as a Carnot heat pump during the other microcycles.

  2. 2.

    Take the example of the system of a cooking vessel, which is brought to a very high temperature in two ways of cooking. Electric resistive coil cooking is an example of heat -exchange process carrying both energy flow and its associated entropy flow; electric induction cooking is an example of (electromagnetic field energy) work -exchange process carrying no entropy flow—with heat generation entropy -production process taking place inside cooking vessel. Entropy gain in the former case results from entropy in-flow across the boundary of the vessel and in the latter case from entropy production within the boundary.

  3. 3.

    The engineering connection is particularly strong in North British: “North British group of scientists and engineers, including James Joule, James Clerk Maxwell, William and James Thomson, Fleeming Jenkin, and P. G. Tait, developed energy physics to solve practical problems encountered by Scottish shipbuilders and marine engineers” noted Smith [14].


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Correspondence to Lin-Shu Wang .

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Wang, LS. (2020). Entropy and the Entropy Principle. In: A Treatise of Heat and Energy. Mechanical Engineering Series. Springer, Cham.

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