Question

I know that this question has many other variations on this site, but I'm trying to see if I understood Helmholtz and Gibbs energy properly or not. The material I'm reading from is Physical chemistry by Thomas Engel and Philip Reid, third edition, and An introduction to Thermal Physics by Daniel Schroeder.

In Schroeder's book, Chapter 5, the author defined Helmholtz energy, A, as A=U−TS, where, U is internal energy of the system and S is the system's final entropy.

The author says that, It is the total energy needed to create the system minus the heat you can get free from the environment at temperature T. He further states that it is the available or free energy.

Then, for a system in constant pressure (P) and temperature (T) environment, he defines Gibbs energy, G, as G=U−TS+PV, where PV is the atmospheric work term that's in enthalpy,
H = U + PV.
Also, from Engel and Reid, chapter 6, we have, for isothermal process,

dA ≤ đwtotal ... (1), including expansion and non-expansion work, where the equality is satisfied for reversible process. Equation (1) allows us a way to calculate maximum work that a system can do on the surroundings. And in a similar manner dG ≤ đwnon−expansion .... (2), where the equality is satisfied for reversible process.
It is stated that equation (2) allows one to calculate maximum non-expansion work that can be produced.
Now, this is my understanding:
For reversible process, A represents total available internal energy, and a part of A, which is G, is the available energy to do non-expansion work.For irreversible processes the inequalities (1) and (2) gives the lower bound for expansion and non-expansion work respectively. Is it the correct way of understanding or am I way off? Also, if A does represent total available internal energy for reversible process then what does it represent for irreversible process? Thanks in advance

Answer 1

Your understanding of Helmholtz and Gibbs free energy seems correct. Helmholtz free energy is the internal energy available for work, and Gibbs free energy is for non-expansion work, with both applying to reversible processes. Irreversible processes have lower actual work done due to inefficiencies and these 'free energies' become maximum work potentials rather than actuals.

Step-by-step explanation:

You seem to have a solid understanding of Helmholtz and Gibbs free energy. For reversible processes, the Helmholtz free energy (A) does indeed represent the total available internal energy that can be converted into work.

You correctly identified that Gibbs free energy (G) is the energy available to do non-expansion work under constant pressure and temperature conditions. This is particularly useful in chemical reactions and phase transitions where the pressure and temperature don't change.

For irreversible processes, the situation is a bit different. The inequalities you've stated, dA ≤ đwtotal and dG ≤ đwnon-expansion, indicate that the actual work done by the system is less than the maximum work predicted by A and G for reversible processes.

The difference is essentially due to the dissipated energy as a result of irreversible processes generating entropy. So for irreversible processes, A does not represent the total available energy for work, because some of the energy is 'lost' to dissipation and cannot be used for work.

Similarly, G represents the maximum non-expansion work that could be done in an ideal, reversible scenario; in reality, less work is obtained due to irreversibilities.

As for Gibbs free energy, it is important to remember that it is not a conserved quantity like internal energy (U) or enthalpy (H), and does not represent the energy content of a system, but rather the potential to perform work.

A negative change in Gibbs free energy (ΔG) indicates a spontaneous process, as the system can do work on the surroundings, whereas a positive ΔG indicates a non-spontaneous process.