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Thermodynamic Systems01:06

Thermodynamic Systems

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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of  tea boiling in a kettle. The...
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Space-Time Curvature and the General Theory of Relativity01:17

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In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
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Statements of the Second Law of Thermodynamics01:15

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The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius’ statement of the second law of thermodynamics is based on the irreversibility of spontaneous heat flow. It states that heat will not flow from the colder body to the hotter body unless some other process is involved. Additionally, as per the Kelvin’s statement, it is impossible to convert the heat from a single source into work without any other...
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Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

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Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
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The First Law of Thermodynamics01:13

The First Law of Thermodynamics

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The first law of thermodynamics deals with the total amount of energy in the universe. It states that this total amount of energy is constant. In other words, there has always been, and always will be, exactly the same amount of energy in the universe. Energy exists in many different forms. According to the first law of thermodynamics, energy may transfer from place to place or transform into different forms, but it cannot be created or destroyed. The transfers and transformations of energy...
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First Law of Thermodynamics01:17

First Law of Thermodynamics

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A change in the internal energy of a system depends on the the net heat transfer into the system and the net work done by the system. The first law of thermodynamics, which is a generalized form of energy conservation, relates these three quantities mathematically. It states that the change in the internal energy equals the difference between the heat transfer and work done by the system.
The applied heat increases the internal energy of a system. Hence, conventionally heat is considered...
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Updated: Jul 21, 2025

Thermocapillary Convection Space Experiment on the SJ-10 Recoverable Satellite
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Geometrothermodynamic Cosmology.

Orlando Luongo1,2,3,4,5, Hernando Quevedo6,7

  • 1Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy.

Entropy (Basel, Switzerland)
|July 29, 2023
PubMed
Summary
This summary is machine-generated.

Geometrothermodynamics unifies geometry and thermodynamics, handling Legendre transformations geometrically. This formalism generates cosmological models from fundamental equations, explaining cosmic inflation and standard cosmology.

Keywords:
fundamental equationsgeometrothermodynamicsrelativistic cosmology

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Area of Science:

  • Thermodynamics
  • Differential Geometry
  • Cosmology

Background:

  • Classical thermodynamics relies on Legendre transformations for potential invariance.
  • Geometric formalisms offer new perspectives on thermodynamic systems.
  • Relativistic cosmology seeks fundamental equations to describe the universe.

Purpose of the Study:

  • To review and elaborate on the geometrothermodynamics formalism.
  • To demonstrate its application in handling thermodynamic potential invariance.
  • To show its utility in generating cosmological models via variational principles.

Main Methods:

  • Utilizing contact and Riemannian geometry to model thermodynamic systems.
  • Applying geometric methods to analyze Legendre invariance.
  • Employing variational principles to derive fundamental thermodynamic equations.

Main Results:

  • Geometrothermodynamics geometrically handles Legendre transformations, ensuring potential independence.
  • A variational principle within this formalism generates fundamental equations.
  • These equations can be applied to relativistic cosmology, yielding models with arbitrary parameters.

Conclusions:

  • Geometrothermodynamics provides a powerful geometric framework for thermodynamics.
  • The formalism successfully generates cosmological models, including those matching inflationary and standard paradigms.
  • This approach offers a unified perspective on thermodynamics and cosmology.