Grand potential

From Wikipedia, the free encyclopedia

There are very few or no other articles that link to this one.
Please help introduce links in articles on related topics. After links have been created, remove this message.
This article has been tagged since September 2006.

This article or section is in need of attention from an expert on the subject.
WikiProject Physics or the Physics Portal may be able to help recruit one.
If a more appropriate WikiProject or portal exists, please adjust this template accordingly.

The grand potential is a quantity used in statistical mechanics, especially for irreversible processes in open systems.

Grand potential is defined by

$\Phi_{G} \ \stackrel{\mathrm{def}}{=}\ E - T S - \mu N$

Where E is the energy, T is the temperature of the system, S is the entropy, μ is the chemical potential, and N is the number of particles in the system.

The change in the grand potential is given by

d Φ G = - S d T - N d μ - P d V

Where P is pressure and V is volume.

When the system is in thermodynamic equilibrium, Φ_G is a minimum. This can be seen by considering that dΦ_G is zero if the volume is fixed and the temperature and chemical potential have stopped evolving.

For an ideal gas,