A Perfect Engine

Consider a two cycle engine. The first process is an adiabatic compression and the second process is a straight line in the PV diagram. The change in internal energy for the cycle must be zero by the definition of a cycle. The work for the cycle is the area of the enclosed space and it is positive because the cycle is clockwise in the PV diagram. The total heat for the cycle must be equal to the total work by the first law of thermodynamics and is therefore also positive. Since the heat for an adiabatic process is zero by definition, this heat must come in during the unnamed process. Since this value of heat is positive, it can be called Q_H. By the definition of efficiency, the efficiency is 1 since W = Q_H. But this must be impossible by the second law of thermodynamics. What gives?

a) It is not true that the change in internal energy for the cycle must be zero by the definition of a cycle.

b) It is not true that he work for the cycle is the area of the enclosed space and it is positive because the cycle is clockwise in the PV diagram.

c) It is not true that 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) It is not true that since the heat for an adiabatic process is zero by definition, this heat must come in during the unnamed process.

e) It is not true that since this value is of heat is positive, it can be called Q_H.

f) It is not true that by the definition of efficiency, the efficiency is 1 since W = Q_H.

Answer

Last updated February 16, 2006
by Erik Jensen