The work-energy theorem is simply a statement of the first law of
thermodynamics for processes in which work is done on a system which
is thermally isolated from its surroundings (adiabatic processes, as
they are called). In the most common case this theorem is employed in
cases where a further hypothesis, that no dissipative processes act in
the working or within the system. (These processes are properly called
"reversible adiabatic processes".) Given these two restrictions on the
types of processes, it is the case that the work done on a system is
equal to the sum of all of the mechanical energy changes that take
place within a system. These may include translational and rotational
kinetic energies, gravitational potential energy*, elastic potential
energy, even energies which manifest themselves by an increase in the
temperature of some part of the system, in which case that part must,
of course, be thermally isolated from other parts**.
Leigh
*It should be recognized that gravitational potential energy of the
mgh sort is a convenient fiction when treated in this way. What one is
really doing is accounting for work done on the Earth-mass system
without formally acknowledging the presence of the Earth.
**I'm thinking about, for example, the energy stored in one of those
gas springs that hold up the rear lid of a hatchback or minivan. This
is gas which is subjected to (ideally reversible) compression and
expansion, and which changes in temperature in consequence. When you
open the hatchback the gas expands and cools, the work that is done on
the outside world in lifting the hatchback was derived at the expense
of the internal energy of the gas in the gas spring, which cools as a
consequence. In the real world it soon warms to ambient temperature,
of course.