Partition function concept

  • B
  • Thread starter soumobrata
  • Start date
  • #1
What is the difference between micro canonical Partition function and canonical Partition function???
Is the mathematical expression of the above two Partition function are same?
If it is then why??
[emoji29]
 

Answers and Replies

  • #2
stevendaryl
Staff Emeritus
Science Advisor
Insights Author
8,401
2,581
As I understand it, the various types of ensembles differ in what is held constant, and what is allowed to change (by exchanging something with the environment--energy, or particles, or whatever). The microcanonical ensemble holds the following quantities fixed:
  1. Total Energy
  2. Volume
  3. Number of particles (of each type)
For a canonical ensemble, instead of holding the total energy constant, the temperature is held constant.

The expressions for the partition function definitely are different in the two cases. The canonical partition function, [itex]Z(N,V,T)[/itex] is a function of T, V, and N, while the microcanonical partition function, [itex]\Omega(N,V,E)[/itex] is a function of E, V and N. The microcanonical partition function is usually called the "density of states". They are related to thermodynamic quantities:

[itex]Z = e^{-A/kT}[/itex] where [itex]A[/itex] is the Helmholtz free energy, [itex]A = E - TS[/itex].
[itex]\Omega = e^{S/k}[/itex] where [itex]S[/itex] is the entropy
 
  • Like
Likes soumobrata
  • #3
Thanks i will show u a problem tomorrow...then my doubts wiil be clear!!
 

Related Threads on Partition function concept

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
0
Views
2K
Replies
1
Views
869
  • Last Post
Replies
1
Views
2K
Replies
1
Views
2K
Replies
9
Views
4K
  • Last Post
Replies
8
Views
1K
Top