5
Entropy and the Entropy Principle
Abstract
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.
Keywords
The first Clausius theorem Á The second Clausius theorem (Clausius’ Inequality) Á
Entropy Á The entropy principle Á Gibbs U-V-S surface Á Entropy functions for
ideal gases ÁApproximateentropyfunctionsforliquids/solidsÁDefinitionofheatÁ
Carnot vapor cycle ÁPropertiesofidealgasmixtures(Gibbs’theorem)ÁReversible
mixing of ideal gases Á Birth of equilibrium thermodynamics
5.1 What Determines the Direction of Natural Processes?
Kelvin made use of the conception of energy to serve the purpose of determining the
direction of natural processes. Opinion may still be divided with regards to whether
dissipation of energy is universal or not, but the matter was already clear to Planck,
© Springer Nature Switzerland AG 2020
L.-S. Wang, A Treatise of Heat and Energy, Mechanical Engineering Series,
https://doi.org/10.1007/978-3-030-05746-6_5
91
Entropy and the Entropy Principle
Abstract
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.
Keywords
The first Clausius theorem Á The second Clausius theorem (Clausius’ Inequality) Á
Entropy Á The entropy principle Á Gibbs U-V-S surface Á Entropy functions for
ideal gases ÁApproximateentropyfunctionsforliquids/solidsÁDefinitionofheatÁ
Carnot vapor cycle ÁPropertiesofidealgasmixtures(Gibbs’theorem)ÁReversible
mixing of ideal gases Á Birth of equilibrium thermodynamics
5.1 What Determines the Direction of Natural Processes?
Kelvin made use of the conception of energy to serve the purpose of determining the
direction of natural processes. Opinion may still be divided with regards to whether
dissipation of energy is universal or not, but the matter was already clear to Planck,
© Springer Nature Switzerland AG 2020
L.-S. Wang, A Treatise of Heat and Energy, Mechanical Engineering Series,
https://doi.org/10.1007/978-3-030-05746-6_5
91