Question

The change in __________ is the amount of energy in a system that is available to do work.

Answer 1

The answer is free energy.
In fact, in thermodynamics, the free energy of a system is defined as the energy that can be converted to do work. Helmholtz definition of free energy, for instance, is:
$A=U-TS$
where U is the internal energy, T the temperature and S is the entropy