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Related Concept Videos

Gibbs Free Energy02:39

Gibbs Free Energy

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One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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An Introduction to Free Energy01:05

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How can we compare the energy that releases from one reaction to that of another reaction? We use a measurement of free energy to quantitate these energy transfers. Scientists call this free energy Gibbs free energy (abbreviated with the letter G) after Josiah Willard Gibbs, the scientist who developed the measurement. According to the second law of thermodynamics, all energy transfers involve losing some energy in an unusable form such as heat, resulting in entropy. Gibbs free energy...
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Gibbs Free Energy and Thermodynamic Favorability02:23

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The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
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Free Energy01:21

Free Energy

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Free energy—abbreviated as G for the scientist Gibbs who discovered it—is a measurement of useful energy that can be extracted from a reaction to do work. It is the energy in a chemical reaction that is available after entropy is accounted for. Reactions that take in energy are considered endergonic and reactions that release energy are exergonic. Plants carry out endergonic reactions by taking in sunlight and carbon dioxide to produce glucose and oxygen. Animals, in turn, break...
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Free Energy and Equilibrium00:55

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The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔG is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
The reaction quotient, Q, is a convenient measure of the...
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Free Energy and Equilibrium02:56

Free Energy and Equilibrium

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The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
Recall that Q is the numerical value of the mass action...
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Gibbs volume entropy is incorrect.

Robert H Swendsen1, Jian-Sheng Wang2

  • 1Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
PubMed
Summary
This summary is machine-generated.

This study confirms negative temperature is a valid thermodynamic concept by showing equilibrium thermodynamic entropy involves a surface integral in phase space. It refutes claims that Gibbs entropy is correct and negative temperatures are invalid.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • The validity of negative absolute temperatures in thermodynamics remains a subject of debate.
  • Recent studies have challenged the extension of thermodynamics to include negative temperatures, proposing Gibbs entropy as the correct definition.

Purpose of the Study:

  • To demonstrate that equilibrium thermodynamic entropy is correctly expressed as a surface integral in phase space.
  • To validate negative temperature as a legitimate thermodynamic concept.
  • To refute claims that Gibbs entropy is the correct definition and that negative temperatures are invalid.

Main Methods:

  • Derivation of the expression for equilibrium thermodynamic entropy.
  • Analysis of the integral over phase space (surface vs. volume).
  • Comparison of thermodynamic predictions based on different entropy formulations.

Main Results:

  • The equilibrium thermodynamic entropy is shown to contain a surface integral in phase space.
  • Negative temperature is confirmed as a valid thermodynamic concept.
  • The Gibbs entropy, formulated with a volume integral, is shown to be incorrect and fails to satisfy thermodynamic postulates.

Conclusions:

  • The correct formulation of thermodynamic entropy supports the physical reality of negative temperatures.
  • The Gibbs entropy definition is inadequate for systems exhibiting non-monotonic energy densities of states.
  • This work resolves the controversy surrounding negative temperatures in thermodynamics.