Isothermal–isobaric ensemble

Statistical mechanics
Microcanonical ensemble
Canonical ensemble
Grand canonical ensemble
Isothermal–isobaric ensemble
Isoenthalpic–isobaric ensemble
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The isothermal–isobaric ensemble (constant temperature and constant pressure ensemble) is a statistical mechanical ensemble that maintains constant temperature $T \,$ and constant pressure $P \,$ applied. It is also called the $N p T$ -ensemble, where the number of particles $N \,$ is also kept as a constant. This ensemble plays an important role in chemistry as chemical reactions are usually carried out under constant pressure condition. The partition function can be written as the weighted sum of the paritition function of canonical ensemble, $Z(N, V, T) \,$ .

$\Delta(N, P, T) = \int Z(N, V, T) \exp(-\beta PV ) C dV. \,\;$

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where $\beta=1/k_B T \,$ ( $k_B \,$ is Boltzmann factor), and $V\,$ is volume of the system.

There are several candidates for the normalization factor $C \,$ , e.g., $C=N/V\,$ , or $C=\beta P \,$ . These choices make the partition function a nondimensional quantity. The differences vanish in the thermodynamic limit, i.e., in the limit of infinite number of particles.