Grand Potential - Definition

Definition

Grand potential is defined by


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

where U is the internal 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

\begin{align}
d\Phi_{G} & = dU - TdS - SdT - Nd\mu \\
& = - P dV - S dT - N d\mu
\end{align}

where P is pressure and V is volume, using the fundamental thermodynamic relation (combined first and second thermodynamic laws);

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

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