Gibbs Energy Change and Maximum Work

[NK92]

Homework Statement

I am trying to understand the implications of the principle that the maximum non-expansion work, dw_add is equal to the Gibbs energy change for a reversible process.

Homework Equations

For a reversible process, dw_add = dG.

This is provided that the process takes place at constant pressure and temperature.

The Attempt at a Solution

The source of my confusion is to do with the fact that if the Gibbs energy change of a system, dG, is zero at constant temperature and pressure, then that system is at equilibrium. When a system undergoes a reversible change, it passes through a series of equilibrium states before attaining its final state. Hence, for a reversible process,

dG = 0

But, dG = dw _add

So that seems to imply that for any reversible process, the non-expansion work available is always zero, which doesn't seem to be true.

Would greatly appreciate any clarifications. Thanks in advance.

 

[nate808]

Thank you for your question. The principle that the maximum non-expansion work is equal to the Gibbs energy change for a reversible process can be a bit confusing, but I will try to explain it in more detail for you.

Firstly, it is important to remember that the Gibbs energy, G, is a state function, meaning it only depends on the initial and final states of a system, not the path it takes to get there. This means that for a reversible process, the change in Gibbs energy, dG, will be the same whether the process is carried out reversibly or irreversibly.

Now, let's consider the definition of non-expansion work, dw add. This is the work done on or by a system due to processes other than expansion or compression. In other words, it is the work done due to changes in other forms of energy, such as chemical or electrical energy.

For a reversible process, the maximum non-expansion work would be the work done when the process is carried out reversibly. This is because in a reversible process, all energy transformations are carried out without any loss of energy. Therefore, the maximum non-expansion work, dw add, is equal to the Gibbs energy change, dG.

However, this does not mean that the non-expansion work is always zero for a reversible process. It simply means that the maximum non-expansion work that can be obtained from a reversible process is equal to the Gibbs energy change. In fact, for a reversible process, the non-expansion work can be any value, as long as it does not exceed the Gibbs energy change.

I hope this helps to clarify the principle for you. Remember, for a reversible process, dG = dw add only if the process is carried out at constant temperature and pressure. If the process is not carried out under these conditions, then the maximum non-expansion work may not be equal to the Gibbs energy change.

Best of luck with your studies!