Quick question about Gibbs free energy

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In the Gibbs free energy equation G = U - TS + pV, T and p refer to the system's temperature and pressure, not necessarily the environment's. For Gibbs free energy to be defined, the system should ideally be in thermal and mechanical equilibrium with its surroundings, which means it can have the same temperature and pressure as the environment. When in this equilibrium, the Gibbs free energy reaches its minimum value. The confusion arises from the interpretation of pressure in the context of work done on the system, where p can be seen as the pressure from the surroundings. Understanding these relationships is crucial for accurately applying thermodynamic principles.
Zarquon
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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.
 
Thanks.
Part of the reason for my confusion is this page:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/helmholtz.html
Seems to me that the "work to give the system final volume V at constant pressure p" should be equal to pV where p is the pressure from the surroundings?
 
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