Grand canonical ensemble: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
mNo edit summary
Line 26: Line 26:
* <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>


== Free energy and Partition Function ==
== Free energy and Partition Function ==
== Free energy and Partition Function ==


The  [[Helmholtz energy function]] is related to the canonical partition function via:
(THis subsection should be checked)
 
The  Corresponding thermodynamic potentail for the Grand Canonical Partition function is:
 
: <math> \left. A - \mu N \right. </math>, i.e.:
 
 
:<math> \left. p V = k_B T \log Q_{\mu V T } \right. </math>


:<math> A\left(N,V,T \right) = - k_B T \log  Q_{NVT} </math>
[[Category:Statistical mechanics]]
[[Category:Statistical mechanics]]

Revision as of 16:20, 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

(THis subsection should be checked)

The Corresponding thermodynamic potentail for the Grand Canonical Partition function is:

, i.e.: