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Related Concept Videos

Calculating Standard Free Energy Changes02:49

Calculating Standard Free Energy Changes

The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
Free Energy and Equilibrium02:56

Free Energy and Equilibrium

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 expression...
Free Energy and Equilibrium00:55

Free Energy and Equilibrium

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 status of an...
Gibbs Free Energy and Thermodynamic Favorability02:23

Gibbs Free Energy and Thermodynamic Favorability

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:
Gibbs Free Energy02:39

Gibbs Free Energy

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...
Effects of Temperature on Free Energy02:11

Effects of Temperature on Free Energy

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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Related Experiment Video

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Differential Scanning Calorimetry &#8212; A Method for Assessing the Thermal Stability and Conformation of Protein Antigen
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Differential Scanning Calorimetry — A Method for Assessing the Thermal Stability and Conformation of Protein Antigen

Published on: March 4, 2017

Nonequilibrium free-energy relations for thermal changes.

Stephen R Williams1, Debra J Searles, Denis J Evans

  • 1Research School of Chemistry, The Australian National University, Canberra, ACT 0200, Australia.

Physical Review Letters
|July 23, 2008
PubMed
Summary

This study generalizes the Jarzynski equality and Crooks fluctuation theorem to calculate free energy changes from nonequilibrium processes driven by thermal or mechanical agents. The findings are applicable to experimental setups involving temperature changes.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Physical Chemistry

Background:

  • The Jarzynski equality and Crooks fluctuation theorem relate equilibrium free energy changes to nonequilibrium work performed on a system.
  • These theorems traditionally apply to systems driven by mechanical external agents while in contact with a thermal reservoir at constant temperature.

Purpose of the Study:

  • To generalize existing fluctuation theorems for free energy calculations.
  • To extend the applicability of these theorems to processes driven by arbitrary external agents, including thermal ones.
  • To adapt the generalized relations for experimental measurements, particularly those involving temperature changes.

Main Methods:

  • Theoretical generalization of nonequilibrium path integral formulations.
  • Analysis of systems driven by both mechanical and thermal external agents.
  • Derivation of new relations applicable to heat reservoir-driven processes.

Main Results:

  • Established generalized Jarzynski equality and Crooks fluctuation theorem for mixed thermal-mechanical driving.
  • Developed a framework to compute free energy changes from systems undergoing temperature variations.
  • Formulated results in a manner suitable for direct experimental implementation.

Conclusions:

  • The generalized theorems provide a broader scope for calculating free energy changes in nonequilibrium systems.
  • This work extends the utility of fluctuation theorems beyond purely mechanical driving.
  • The derived relations offer practical tools for experimental investigations in thermodynamics and statistical physics.