Consider the two process engine above. The first process is an adiabatic compression (blue) and the second process is a straight line in the PV diagram (red). The efficiency can be determined based on the following assertions:

A) The change in thermal energy for the cycle must be zero by the definition of a cycle.

B) The work output for the cycle is the area of the enclosed space and it is positive because the cycle is clockwise in the PV diagram.

C) The total heat for the cycle must be equal to the total work by the first law of thermodynamics and is therefore also positive.

D) Since the heat for an adiabatic process is zero by definition, this heat must come in only during the unnamed process.

E) Since this value of heat is positive, it can be called Q_H.

F) By the definition of efficiency, the efficiency is 1 since W = Q_H.

G) But the previous assertion must be impossible by the second law of thermodynamics.

Which is the first faulty assertion?

Solution: E. Typically, a process will either add or remove heat, but in some unnamed processes with a negative slope in the PV diagram, it can be shown that the heat is positive for a portion and negative for a portion. The heat in the above described process will be positive when it is less steep than an adiabatic curve and negative when it is more steep than an adiabatic curve. The heat for that process is the net heat, |Q_H| - |Q_C|,not the heat input, Q_H. To determine the heat input, the work must be added to the magnitude of the heat output (which is very tricky to determine in this case).