How is the maximum work derived from the Helmholtz energy described?

The maximum work derived from the Helmholtz energy, denoted as ( w_{max} ), is appropriately expressed as ( w_{max} = \Delta A ). The Helmholtz free energy (( A )) is a thermodynamic potential that is particularly useful in systems at constant temperature and volume. It is defined as:

[

A = U - TS

]

where ( U ) is the internal energy, ( T ) is the absolute temperature, and ( S ) is the entropy. The change in Helmholtz free energy (( \Delta A )) during a process indicates the maximum amount of work obtainable from a system when it undergoes a reversible process at constant temperature and volume.

This concept follows from the second law of thermodynamics and implies that when a system does work, it does so at the expense of energy that contributes to changes in ( A ). Therefore, if a process leads to a decrease in Helmholtz free energy (( \Delta A < 0 )), it signifies that the system can perform useful work.

In summary, the relationship between the change in Helmholtz energy and the maximum work obtainable from a thermodynamic process at constant temperature and volume is why