# Helmholtz free energy question

1. Dec 8, 2005

### asdf1

what's the physical meaning of that equation? all i see is a jumble of numbers and equations...

2. Dec 8, 2005

### StatusX

Are you talking about the equation for a specific system, because if so, you'll need to tell us what it is if you want help. In general, the helmholtz free energy is A=U-TS, where U is the internal energy, T is the temperature, and S is the entropy. This is hardly a jumble of numbers, hence my first comment. It is the function that is minimized at equilibrium for a system held at constant volume and temperature. It is also easily calculated from statistical mechanics by A=-kT ln(Z), where Z is the partition function.

3. Dec 9, 2005

### asdf1

what do you usually use that equation for?

4. Dec 9, 2005

### StatusX

Like I said, it is the thermodynamic potential (ie, the function that is minimized at equilibrium) for any system held at constant temperature and volume. So you would calculate the free energy and then minimize it with respect to each free variable to find the equilibrium position of the constrained system. It is also used to calculate various other thermodynamic quantities starting from a statistical model of the system, since it is the thermodynamic quantity most easily obtained from statistical methods (more specifically, the canonical ensemble).

5. Dec 10, 2005

### asdf1

thank you very much!!! :)