Tru Physics

Gibbs Free Energy

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Tru Physics
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Introduction

Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. It is a useful concept in the field of thermodynamics and is especially relevant in processes such as chemical reactions, phase transitions, and solution formation.

Definition

Gibbs free energy is defined as:

G = H - TS

where:

  • G is the Gibbs free energy,
  • H is the enthalpy,
  • T is the absolute temperature, and
  • S is the entropy of the system.

Gibbs Free Energy and Spontaneity

Gibbs free energy is intimately connected with the spontaneity of a process. The change in Gibbs free energy (\Delta G) during a process is given by:

\Delta G = \Delta H - T \Delta S

where \Delta H is the change in enthalpy and \Delta S is the change in entropy. If \Delta G is negative, the process occurs spontaneously. If \Delta G is positive, the process is non-spontaneous, and if \Delta G is zero, the system is in equilibrium.

Gibbs Free Energy and Chemical Reactions

In a chemical reaction at constant temperature and pressure, the change in Gibbs free energy is given by:

\Delta G = \Delta G^\circ + RT \ln(Q)

where:

  • \Delta G is the change in Gibbs free energy,
  • \Delta G^\circ is the standard change in Gibbs free energy,
  • R is the ideal gas constant,
  • T is the absolute temperature, and
  • Q is the reaction quotient.

\Delta G^\circ can be calculated from the standard Gibbs free energies of formation (\Delta G_f^\circ) of the reactants and products:

\Delta G^\circ = \Sigma \nu_p \Delta G_{f,p}^\circ - \Sigma \nu_r \Delta G_{f,r}^\circ

where \nu_p and \nu_r are the stoichiometric coefficients of the products and reactants, respectively.

Gibbs Energy and Phase Transitions

Gibbs free energy is also crucial for understanding phase transitions. For a phase transition at constant temperature and pressure, the change in Gibbs free energy is given by:

\Delta G = \Delta H - T \Delta S = 0

where \Delta H is the enthalpy change of the transition and \Delta S is the entropy change of the transition. This is because at equilibrium (where phase transitions occur), \Delta G = 0.

Conclusion

Gibbs free energy is a fundamental concept in thermodynamics. It relates the energy, entropy, and enthalpy of a system and provides a criterion for the spontaneity of processes. Understanding the Gibbs free energy is essential for many fields, including physics, chemistry, engineering, and materials science.

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