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| {{Unreferenced|date=December 2009}}
| | The author is called Wilber Pegues. What me and my family love is doing ballet but I've been taking on new things recently. Kentucky is where I've usually been living. Credit authorising is exactly where my primary earnings comes from.<br><br>Feel free to surf to my weblog; [http://Www.Youronlinepublishers.com/authWiki/AdolphvhBladenqq free psychic readings] |
| {{Statistical mechanics|cTopic=[[Statistical ensemble (mathematical physics)|Ensembles]]}}
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| The '''isothermal–isobaric ensemble''' (constant temperature and constant pressure ensemble) is a statistical mechanical ensemble that maintains constant temperature <math>T \,</math> and constant pressure <math>P \,</math> applied. It is also called the <math>NpT</math>-ensemble, where the number of particles <math>N \,</math> 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 partition function of [[canonical ensemble]], <math>Z(N, V, T) \,</math> . | |
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| :<math>\Delta(N, P, T) = \int Z(N, V, T) \exp(-\beta PV ) C dV. \,\;</math>
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| where <math>\beta=1/k_B T \, </math> (<math>k_B \,</math> is the [[Boltzmann constant]]), and <math>V\,</math> is volume of the system.
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| There are several candidates for the normalization factor <math>C \, </math>, e.g., <math>C=N/V\, </math>, or <math>C=\beta P \, </math>. These choices make the partition function a [[nondimensionalization|nondimensional]] quantity. The differences vanish in the [[thermodynamic limit]], i.e., in the limit of infinite number of particles.
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| The characteristic state function of this ensemble is the [[Gibbs free energy]],
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| :<math>G(N, P, T) = - k_B T \ln \Delta(N, P, T) \;\, </math>
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| This thermodynamic potential is related to the [[Helmholtz free energy]] (logarithm of the canonical partition function), <math>F\,</math>, in the following way:
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| :<math> G = F+PV. \;\, </math>
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| {{Statistical mechanics topics}}
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| {{DEFAULTSORT:Isothermal-Isobaric Ensemble}}
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| [[Category:Statistical ensembles]]
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| {{Physics-stub}}
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The author is called Wilber Pegues. What me and my family love is doing ballet but I've been taking on new things recently. Kentucky is where I've usually been living. Credit authorising is exactly where my primary earnings comes from.
Feel free to surf to my weblog; free psychic readings