- #1
Narcol2000
- 25
- 0
What is the reasoning behind defining the helmholtz free energy as F = -kT ln Z?
I always wanted to know why it was just defined as the above. Is it as a form of convenience because the macroscopic theromodynamic observables of a system at constant temperature (ie the canonical ensemble) are related to to the partition function as ln Z?
ie.
[tex]
\bar{E} = -\frac{\partial lnZ}{\partial \beta}
[/tex]
and
[tex]
P = \frac{1}{\beta}\left(\frac{\partial lnZ}{\partial V}\right)_\beta
[/tex]
So its just convenient to a create a thermodynamic quantity that is related to T ln Z for a system at temperature T?
I always wanted to know why it was just defined as the above. Is it as a form of convenience because the macroscopic theromodynamic observables of a system at constant temperature (ie the canonical ensemble) are related to to the partition function as ln Z?
ie.
[tex]
\bar{E} = -\frac{\partial lnZ}{\partial \beta}
[/tex]
and
[tex]
P = \frac{1}{\beta}\left(\frac{\partial lnZ}{\partial V}\right)_\beta
[/tex]
So its just convenient to a create a thermodynamic quantity that is related to T ln Z for a system at temperature T?