Understanding Carnot's Cycle & Reversible Processes

[anigeo]

Why is it so that along with reversible isothermic processes , reversible adiabatic processes must be taken up to complete carnot's cycle?

 

[Andrew Mason]

Why is it so that along with reversible isothermic processes , reversible adiabatic processes must be taken up to complete carnot's cycle?

There are two things that are required of a Carnot cycle:

1. In order to be reversible, heat flow must only occur where there is an infinitessimal temperature difference between the system and the reservoirs. So all heat flow must be isothermal.

2. In order to make it a complete cycle, the isothermal expansion must be followed by some kind of compression.

If there was an isothermal compression that started at the end point of the isothermal expansion, there would be no net work done. The compression has to require less work to accomplish than the work that is done on the isothermal expansion. This means the temperature has to decrease before the compression can begin. Since heat flow has to occur with an infinitessimal temperature difference, there can be no heatflow as the temperature decreases. So the temperature reducing expansion has to be adiabatic. Thus an adiabatic expansion has to be inserted after the isothermal expansion so that the compression can begin at a lower temperature and require less work to get back to the original state.

Following the adiabatic expansion, isothermal compression begins and is then followed by an adiabatic compression so the first part of the next cycle, the isothermal expansion, can occur at the temperature of the hot reservoir - higher temperature.

AM