Carnot Cycles with Irreversible Heat Transfer
This Demonstration models a Carnot cycle as either a heat engine or a heat pump. Change the temperature differences between the reservoirs and the Carnot cycle with sliders. The entropy changes for the reservoirs ( and ) and the overall entropy change are calculated. When the temperature differences between the reservoirs and the engine/pump are zero, the total entropy change is zero and the process is reversible. The entropy change of the engine/pump, which is at steady state, is zero. All energies and entropy changes are per unit time, since these are continuous processes, but the time scale is arbitrary. The cycle efficiency is calculated for the heat engine, and the coefficient of performance is calculated for the heat pump. As the temperature differences between the reservoirs and the engine/pump increase, the efficiency/coefficient of performance decreases. For the heat engine, is held constant at 1250 J, and for the heat pump, is held constant at 600 J.
Contributed by: Rachael L. Baumann (July 2014)
Additional contributions by: Megan Maguire, John L. Falconer, and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
where and are user-defined differences in reservoir and Carnot cycle temperatures (K). The subscripts and refer to the hot or cold reservoirs, and the subscripts and refer to the hot or cold temperatures of the Carnot cycle. is temperature (K), is the change in entropy (J/K), and is heat gained or lost (J).
For a Carnot heat engine, heat is transferred from a hot reservoir to a cold reservoir and the engine does work (). For a real process, and . The efficiency of a Carnot engine, in terms of the engine temperatures, is:
For a Carnot heat pump, heat is transferred from the cold reservoir to the hot reservoir and work is added. For a real process, and to have a reasonable rate of heat transfer. The coefficient of performance is
The screencast video at  explains how to use this Demonstration.
 J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, New York: Pearson Education, 2012 pp. 157–158.
 Carnot Cycle with Irreversible Heat Transfer. www.colorado.edu/learncheme/thermodynamics/CarnotCycles.html.