This simulation 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 the sliders. The entropy changes for the reservoirs ($\Delta S_h$ and $\Delta S_c$) and the overall entropy change ($\Delta S_{total}$) 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 $\eta$ is calculated for the heat engine, and the coefficient of performance $COP$ 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, $Q_H$ is held constant at 1250 J, and for the heat pump, $Q_C$ is held constant at 600 J.
Note that the $Q_H$ and $Q_C$ values in the figure are relative to the heat engine. That is, if $Q_H$ is negative, it means heat is removed from the heat engine.
where $\Delta T_1$ and $\Delta T_2$ are user-defined differences in reservoir and Carnot cycle temperatures (K). The subscripts $h$ and $c$ refer to the hot or cold reservoirs, and the subscripts $H$ and $C$ refer to the hot or cold temperatures of the Carnot cycle. $T$ is temperature (K), $\Delta S$ is the change in entropy (J/K), and $Q$ 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 ($W$). For a real process, $T_h \geq T_H$ and $T_c \leq T_C$. The efficiency $\eta$ 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, $T_h \leq T_H$ and $T_c \geq T_C$ to have a reasonable rate of heat transfer. The coefficient of performance $COP$ is
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to LearnChemE@gmail.com.