Unconventional cycles and multiple adiabatic points

The so-called unconventional cycles provide a useful didactic resource to discuss the second law of thermodynamics applied to heat engines and their efficiency. In the simplest, previous and thoroughly studied case involving a negatively sloped linear process, interesting physics follow from the presence of an adiabatic point. At such point, the process is tangent to an adiabatic curve and δQ = 0, signalling where the heat flow is reversed. In order to deal with the follow up question on the possibility of having more than one adiabatic point, we introduce a parabolic process whose behavior is richer but still amenable to analytical exploration. In addition, we define pseudoadiabatic processes that are reversible and non-isoentropic, but whose total heat exchanged is zero. These processes are useful when emphasizing the necessary and sufficient conditions for an actual adiabatic process. The linear-parabolic cycle is then introduced, and a few particular cases are discussed. (paper)