Grand canonical ensemble: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
mNo edit summary
Line 16: Line 16:
where:
where:


* <math> \Lambda </math> is the [[de Broglie thermal wavelength]] (depends on the temperature)
*<math> \left. N \right. </math> is the number of particles
 
* <math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]] (depends on the temperature)


* <math> \beta = \frac{1}{k_B T} </math>, with <math> k_B </math> being the [[Boltzmann constant]]
* <math> \beta = \frac{1}{k_B T} </math>, with <math> k_B </math> being the [[Boltzmann constant]]


* <math> U </math> is the potential energy, which depends on the coordinates of the particles (and on the interaction model)
* <math> \left. U \right. </math> is the potential energy, which depends on the coordinates of the particles (and on the interaction model)


* <math> \left( R^*\right)^{3N} </math> represent the 3N position coordinates of the particles (reduced with the system size): i.e. <math> \int d (R^*)^{3N} = 1 </math>
* <math> \left( R^*\right)^{3N} </math> represent the 3N position coordinates of the particles (reduced with the system size): i.e. <math> \int d (R^*)^{3N} = 1 </math>

Revision as of 15:13, 28 February 2007

Ensemble variables

  • Chemical Potential,
  • Volume,
  • Temperature,

Partition Function

Classical Partition Function (one-component system) in a three-dimensional space:

where:

  • is the number of particles
  • , with being the Boltzmann constant
  • is the potential energy, which depends on the coordinates of the particles (and on the interaction model)
  • represent the 3N position coordinates of the particles (reduced with the system size): i.e.

Free energy and Partition Function

Free energy and Partition Function

The Helmholtz energy function is related to the canonical partition function via: