Isothermal-isobaric ensemble: Difference between revisions
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Ensemble variables: | |||
* N (Number of particles) | * N (Number of particles) | ||
* p (Pressure) | * p (Pressure) | ||
* T (Temperature) | * T (Temperature) | ||
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 | ||
| Line 12: | Line 11: | ||
where | where | ||
* <math> \left. V \right. </math> is the Volume: | |||
*<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. \Lambda \right. </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 11:03, 27 February 2007
Ensemble variables:
- N (Number of particles)
- p (Pressure)
- T (Temperature)
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^*)^{3N} \exp \left[ - \beta U \left(V,(R^*)^{3N} \right) \right] }
where
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. V \right. } is the Volume:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta = \frac{1}{k_B T} } ;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \Lambda \right. } is the de Broglie wavelength
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left( R^* \right)^{3N} } represent the reduced position coordinates of the particles; i.e. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int d ( R^*)^{3N} = 1 }
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. U \right. } is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)
References
- D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press