Which concept represents the amount of energy in a system that is unavailable for doing work?

The concept that represents the amount of energy in a system that is unavailable for doing work is entropy. In thermodynamics, entropy is a measure of the disorder or randomness in a system and also indicates the degree of energy dispersal within that system. As entropy increases, the amount of energy that can be converted into work decreases, meaning that high entropy corresponds to a higher portion of energy that is unable to perform useful work.

In contrast, other concepts such as free energy pertain to the energy available to do work, while work energy relates to energy as it is transformed or transferred during the performance of work. Inertia, on the other hand, refers to the resistance of an object to changes in its state of motion and does not have a direct relationship with energy and its availability for work. Therefore, entropy is the most appropriate term to describe energy that cannot be used to perform work, emphasizing the notion of energy inefficiency in systems.