This simulator follows a monatomic ideal-gas piston through the Carnot cycle's four reversible steps — isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression. Switch between heat-engine and refrigerator operation, and reconcile heat, boundary work, internal energy and entropy across every step.
• A real-time 3D piston-cylinder workbench (an ideal-gas chamber, a variable piston load, and switchable hot/cold reservoir connections) with home view, focus-selected-part, auto-rotate, expand, show/hide outer shell and hide-labels scene tools. • Experiment controls: hot reservoir temperature, cold reservoir temperature, gas amount and engine/refrigerator mode selector, plus pause/resume, single-step and 60 s-step buttons, six playback speeds, and restart/run-cycle/stop actions. • A Curves & measurements analysis tab with two live charts (temperature-entropy cycle; cumulative first-law accounting), the underlying ideal-gas process and Carnot-efficiency equations, and snapshot readouts (heat absorbed, heat rejected, net work, thermal efficiency or coefficient of performance, and entropy change per step). • An Experiments tab with four guided fixtures (showing half the absorbed heat becomes work at a 2:1 temperature ratio, adiabatic cooling between the isothermal steps, reversing the cycle into refrigerator mode, and an invalid reservoir order case) and a Model verification bench with a timestamped event log and copyable trial report. • A Learn & assess tab with four guided lessons, a knowledge-check quiz with reset, and a written model-scope statement linking to a Carnot-cycle reference.
The Carnot cycle alternates between isothermal steps (constant temperature, where the gas exchanges heat with a reservoir while the piston moves to keep internal energy unchanged) and adiabatic steps (no heat exchange, where internal energy and temperature change purely from boundary work). Separating these two step types is essential to reading the pressure-volume and temperature-entropy charts correctly — the model's four-step structure keeps them visually and numerically distinct throughout.
Carnot efficiency depends only on the ratio of absolute reservoir temperatures: η = 1 − Tcold/Thot. The half-the-heat-becomes-work experiment demonstrates this directly at a 2:1 temperature ratio, where exactly half of the heat absorbed from the hot reservoir converts to net work — illustrating that efficiency is a temperature ratio, not a property of the gas or the cycle's size.
Because every step in the Carnot cycle is reversible, running the entire sequence backward converts the heat engine into a refrigerator (or heat pump): net work is now supplied to the piston rather than extracted from it, and heat moves from the cold reservoir to the hot reservoir rather than the reverse — the reverse-the-cycle experiment demonstrates this directly using the same equations in the opposite direction. The invalid-reservoir-order experiment shows what happens if the hot reservoir temperature is not actually higher than the cold reservoir's: the cycle cannot proceed as configured, since Carnot's reversible analysis requires TH > TC.
This is a quasistatic, reversible monatomic ideal-gas Carnot cycle with perfect thermal switches, infinite reservoirs and a frictionless variable load; all temperatures are absolute. Process curves and cumulative heat/work use exact analytical formulas in both directions. Twelve animation seconds trace one full cycle — this is illustrative animation time, not physical cycle time or a statement about a finite-power machine. Apparatus dimensions are representative, with piston travel scaled proportionally to volume per trial. The model excludes real-gas effects, leaks, mechanical friction and any finite-rate heat-transfer limitation; animation ends automatically after 100 cycles, and any parameter change resets the state.
Carnot efficiency depends only on the ratio of the absolute hot and cold reservoir temperatures: η = 1 − Tcold/Thot. It does not depend on the working substance, the amount of gas, or the size of the apparatus — only on the two reservoir temperatures.
During isothermal steps, the gas exchanges heat with a reservoir while its temperature stays constant, so internal energy does not change — all absorbed heat converts directly to boundary work. During adiabatic steps, no heat is exchanged at all; temperature and internal energy change purely because of the work done by or on the gas.
Yes — because every step is reversible, running the same sequence backward moves heat from the cold reservoir to the hot reservoir using supplied work, converting the heat engine into an ideal refrigerator or heat pump. The simulator demonstrates this directly with a reverse-the-cycle experiment.
The cycle cannot proceed as a valid Carnot heat engine, since the reversible analysis requires the hot reservoir to be strictly hotter than the cold reservoir. The simulator's invalid-reservoir-order experiment demonstrates this boundary condition directly.