Quick question about Gibbs free energy

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SUMMARY

The discussion clarifies that in the Gibbs free energy equation, G = U - TS + pV, the variables T (temperature) and p (pressure) refer to the conditions of the system itself, not the environment. For Gibbs free energy to be accurately defined, the system must be in thermal and mechanical equilibrium with its surroundings, which means it can exchange heat and work with the environment. The minimum value of Gibbs free energy occurs under these equilibrium conditions, ensuring optimal stability for the system.

PREREQUISITES
  • Understanding of thermodynamic concepts, particularly Gibbs free energy.
  • Familiarity with the laws of thermodynamics, especially thermal and mechanical equilibrium.
  • Knowledge of state functions in thermodynamics, including internal energy (U) and entropy (S).
  • Basic grasp of pressure and volume relationships in thermodynamic systems.
NEXT STEPS
  • Study the derivation of Gibbs free energy and its applications in chemical reactions.
  • Explore the concept of thermal and mechanical equilibrium in detail.
  • Learn about the implications of Gibbs free energy in phase transitions and chemical thermodynamics.
  • Investigate the relationship between Gibbs free energy and Helmholtz free energy.
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This discussion benefits students and professionals in chemistry and physics, particularly those studying thermodynamics, as well as researchers interested in the stability of thermodynamic systems.

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In the expression defining Gibbs free energy,
G = U - TS +pV,
are T and p the temperature and pressure of the environment, or of the system itself? Or is it a requirement that the system has the same temperature and pressure as the environment for the Gibbs free energy to be defined?
 
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T and p describe the system. For a system in thermal equilibirum and mechanical equilibrium with the environment - consider the system surrounded by heat and pressure reservoirs - the Gibbs free energy is at its minimum value.
 

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