# Gibbs-Duhem relation

The **Gibbs-Duhem relation** is given by

or

where is the pressure, is the entropy, is the volume, is the chemical potential and is the number density.

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The **Gibbs-Duhem relation** is given by

- $SdT-Vdp+Nd\mu =0$

or

- $\left.{\frac {\partial p}{\partial \mu }}\right\vert _{T}=\rho$

where $p$ is the pressure, $S$ is the entropy, $V$ is the volume, $\mu$ is the chemical potential and $\rho$ is the number density.