# University of Wisconsin Green Bay

Over one complete cycle, 640 J of heat is put into a heat engine that operates with 50% efficiency. How much work is done by the engine in that cycle?

• In this problem, you are asked about work done by a heat engine. In a heat engine, thermal energy is put in and work is put out. In other words, heat engines can be understood by tracking energy. This is a Conservation of Energy problem.

• Unlike mechanical energy problems, no figure is needed in this case. The heat engine goes through a complete cycle—it returns to its original state. So drawing a picture of the engine will not help you track energy changes.

• Any time you understand the motion of an object by looking at its energy, you begin with a statement of Conservation of Energy.

The First Law of Thermodynamics states Conservation of Energy in the most useful form for heat engines:

ΔQ = ΔU + W

This is the only equation you will need for this problem.

• ΔQ = ΔU + W (1)
320 J = 0 + W (2)
W = 320 J (3)

The heat engine does 320 J of work in one complete cycle. No further mathematical solution is needed for this problem.

• The energy chain for this problem is

Internal energy is not included on the energy chain because it is the same at the end of the cycle as it was at the start.

We know that 640 J of energy are put into the engine and that half of that value is exhaust (50% efficiency.) Therefore, the remaining 320 J of energy go to do work.