Carnot Cycle: Interactive Simulations

These simulations were prepared using Mathematica. Download the free Wolfram player, and then download the simulation CDF file (link given below or click on figure to download). Try to predict the behavior when a parameter changes before using a slider to change that parameter. A screencast below explains how to use the second simulation.

Simulation: Carnot Cycle on Ideal Gas

The Carnot cycle is an idealization for a heat engine operating reversibly between two reservoirs at temperatures T1 and T2 . The working substance is assumed to be one mole of an ideal gas with heat-capacity ratio, γ =CP/CV. The four steps of the cycle are plotted on a pressure-volume diagram, with alternate isotherms (red curves of constant temperature) and adiabatic curves (blue curves of constant entropy). An alternative representation is shown in the insert on a temperature-entropy diagram. A schematic diagram of an idealized heat engine is shown on the right. The sliders enable you to change the heat capacity ratio, temperatures T1 and T2, and the starting and ending volumes in the upper isothermal step.

This simulation was prepared by S. M. Blinder and is located here. Open content licensed under CC BY-NC-SA.

Try to answer these questions before determining the answer with the simulation. We suggest that you write down the reasons for your answers.

  1. How does the pressure versus volume plot change when the cold reservoir temperature increases? When the hot reservoir temperature increases?
  2. How does the efficiency change when the cold reservoir temperature increases?
A sample image for an interactive simulation of the Carnot cycle with an ideal gas.
Simulation: Carnot Cycle with Irreversible Heat Transfer (optional)

This Demonstration shows Carnot cycles operating both as a heat engine and as a heat pump, with finite temperature differences between the hot and cold reservoirs and the high and low temperatures parts of the Carnot cycle, respectively. The entropy changes for the reservoirs, ΔSh and ΔSc, are calculated, as is the overall entropy change ΔStotal. When the temperature differences between the reservoir and the engine/pump are nonzero, the total entropy change is positive. The entropy change of the engine/pump, which is at steady state, is zero. All energies and entropy changes are expressed per unit time, since these are continuous processes, but the time scale is arbitrary. The cycle efficiency η is calculated for the heat engine, and the coefficient of performance (COP) is calculated for the heat pump. As the temperature difference between the reservoirs and the engine/pump increases, the efficiency or the coefficient of performance decreases. For the Carnot heat engine, the value of QH is held constant as the temperature differences change. For the heat pump, the value of QC is held constant as the temperature differences change. For the heat engine, the reservoir temperatures are held constant at 275 K and 500 K. For the heat pump, the reservoir temperatures are held constant at 275 K and 325 K.

Try to answer these questions before determining the answer with the simulation. We suggest that you write down the reasons for your answers.

  1. Does the efficiency of a Carnot heat pump increase or decrease as the temperature difference between the hot reservoir and hot temperature of the cycle increases?
  2. Does the coefficient of performance of a Carnot heat pump increase or decrease when the low temperature of the cycle increases and all other values are held constant?
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