Understanding the Helmholtz free energy, what does 'useful work' really mean?

[zhermes]

When it comes to thermal/statistical mechanics, I'm a little retarded... so bear with me please.

I've used the helmholtz free energy (F) dozens of times, almost as many times as I've heard and read that F is a measure of the 'useful work attainable from a closed thermodynamic system,' at constant temperature and volume. I don't really understand what that means though. How does a closed system even do work when its temperature and volume are fixed (therefore it can't lose heat and can't exert p dV work right?)

Again, I've seen the equations, and heard the lines; but I'm hoping some enlightened and compassionate soul can share their wisdom and philosophical insight to what it all really means.

Thanks!

 

[0xDEADBEEF]

The temperature and volume do not stay constant at the same time. Otherwise F doesn't change.
AFAIK the Helmholtz energy is just a thermodynamical potential and is not necessarily extractable from the system.
Normally "useful work" is anything that does not go into heat.
Maybe this helps maybe not.

 

[zhermes]

The first part helps a lot.
The rest is still a step in the right direction.

Can you (or anyone) give me an example of a system in equilibrium doing 'useful work' equivalent to F?

 

[0xDEADBEEF]

I have this feeling how this whole wording came about. The Gibbs free energy and the Helmholtz free energy are transforms of the total internal energy U. They are basically convex envelopes of U transformed into new coordinates.
What does this mean?
A system always tries to minimize U, just because it tends to not get back the energy it dissipates to its environment. You see for this it doesn't really matter if you add some constant offset only differences are important.
But Gibbs and Helmholtz noticed that in the "real world" the environment tends to keep certain variables constant. For example experiments in air tend to stay at atmospheric pressure and set ups like combustion engines force the medium into a cylinder that cannot change its volume. This changes the energy budget. So they proposed to transform into another potential which would not be the total energy but what they called "free energy". The energy that actually gets transferred when the environment controls things like temperature, or pressure. And I think this is what they mean by 'useful work attainable from a closed thermodynamic system'. The absolute value is not important, only the fact, that you have to calculate the differences in free energy when your system changes and not the total energy because the environment limits how much you can tap into it.