Isothermal-isobaric ensemble: Difference between revisions
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* p (Pressure) | * p (Pressure) | ||
* T (Temperature) | * T (Temperature) | ||
* V (Volume) | |||
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by | The classical partition function, for a one-component atomic system in 3-dimensional space, is given by | ||
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where | where | ||
*<math> \beta = \frac{1}{k_B T} </math>; | *<math> \beta = \frac{1}{k_B T} </math>; | ||
*<math> \Lambda </math> is the '''de Broglie''' wavelength | |||
*<math> \left( R^* \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math> | *<math> \left( R^* \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math> | ||
Revision as of 11:19, 26 February 2007
Variables:
- N (Number of particles)
- p (Pressure)
- T (Temperature)
- V (Volume)
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by
![{\displaystyle Q_{NpT}={\frac {\beta p}{\Lambda ^{3}N!}}\int _{0}^{\infty }dVV^{N}\exp \left[-\beta pV\right]\int d(R^{*})^{3N}\exp \left[-\beta U\left(V,(R^{*})^{3N}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b25a24f7c4f7a7cfa5de491a6d0593a5ed1364b)
where
- ;
- is the de Broglie wavelength
- represent the reduced position coordinates of the particles; i.e.
References
- D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press