What is the reasoning behind defining the helmholtz free energy as F = -kT ln Z?(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Reason behind the definition of Helmholtz free Energy

**Physics Forums | Science Articles, Homework Help, Discussion**