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

• zhermes
In summary, the Helmholtz free energy (F) is a thermodynamic potential that represents the useful work attainable from a closed system at constant temperature and volume. It is a transform of the total internal energy and takes into account the limitations imposed by the environment. This means that in order to calculate work done by a system, one must consider changes in free energy rather than total energy.
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!

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.

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?

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.

The concept of "useful work" in the context of the Helmholtz free energy refers to the maximum amount of work that can be extracted from a closed thermodynamic system at constant temperature and volume. This work is considered useful because it can be harnessed and used to perform tasks or produce useful energy.

In simple terms, the Helmholtz free energy represents the energy that is available to do work in a system. This energy is not limited to just mechanical work, but can also include chemical, electrical, or any other form of work that can be extracted from the system. However, in a closed system, the amount of work that can be extracted is limited by the constraints of constant temperature and volume.

To better understand this concept, it may be helpful to think of the Helmholtz free energy as a measure of the system's potential to do work. Just like how a battery has the potential to power a device, the Helmholtz free energy represents the potential of a closed system to do work. And just like how a battery's potential decreases as it is used, the Helmholtz free energy decreases as the system undergoes changes and releases energy.

So, in summary, the term "useful work" in the context of the Helmholtz free energy refers to the maximum amount of work that can be extracted from a closed system at constant temperature and volume. It is a measure of the system's potential to do work, and this work can take on various forms depending on the system's properties and constraints.

## 1. What is the Helmholtz free energy and why is it important?

The Helmholtz free energy is a thermodynamic potential that describes the maximum amount of mechanical work that can be extracted from a system at constant temperature and volume. It is important because it provides insight into the stability and spontaneity of a system, as well as its ability to do useful work.

## 2. What is the difference between Helmholtz free energy and Gibbs free energy?

Both Helmholtz free energy and Gibbs free energy are thermodynamic potentials that describe the maximum amount of work that can be extracted from a system. However, Helmholtz free energy is at constant temperature and volume, while Gibbs free energy is at constant temperature and pressure.

## 3. How is Helmholtz free energy related to entropy?

Helmholtz free energy is related to entropy through the equation F = U - TS, where F is the Helmholtz free energy, U is the internal energy, T is the temperature, and S is the entropy. This equation shows that Helmholtz free energy is related to the extent of disorder in the system, which is represented by entropy.

## 4. What does 'useful work' really mean in the context of Helmholtz free energy?

'Useful work' refers to the work that can be extracted from a system without changing its temperature or volume. In other words, it is the work that can be done without any energy being lost to heat or expansion. This is the maximum amount of work that can be obtained from a system, and it is described by the Helmholtz free energy.

## 5. How can Helmholtz free energy be used in practical applications?

Helmholtz free energy can be used in practical applications to determine the stability and spontaneity of a system, as well as its ability to do work. It can also be used to calculate the maximum work that can be obtained from a system, which is useful in designing and optimizing thermodynamic processes. Additionally, Helmholtz free energy is used in the study of phase transitions and chemical equilibria.

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