The expression for the work done per cycle in terms of the heat extracted from a hot reservoir and the heat delivered to a cold reservoir can be derived from the principles of thermodynamics. It is given by the following equation:
Work per cycle = Heat extracted - Heat delivered
In other words, the work done per cycle is equal to the difference between the heat extracted from the hot reservoir and the heat delivered to the cold reservoir. This expression is based on the first law of thermodynamics, which states that energy is conserved, and it allows us to quantify the conversion of heat into work in a thermodynamic cycle.