I'm looking for an example of a spontaneous process in which a system becomes less ordered and energy becomes less available to do work. what happens to the system’s entropy in this process?
Consider the conduction of heat. From one part to another of a solid conductor.
This is a spontaneous process which leads to higher disordered states than before.
Entropy of the system increases as it does for all spontaneous irreversible processes.
It may be further shown that, the energy that becomes unavailable for work is proportional to the entropy change.
Refer to : Heat and Thermodynamics by Zemansky and Dittman