Thermodynamics
Stirling cycle
Two isotherms + two isochors with regeneration.
Stirling cycle — interactive Thermodynamics simulation. Two isotherms + two isochors with regeneration. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Stirling cycle
Two isotherms + two isochors with regeneration.
The Stirling cycle uses a regenerator to store heat during constant-volume steps and return it later, approaching Carnot-like performance in an ideal design. Real Stirling engines trade complexity for quieter operation and flexible heat sources.
- Two isotherms + regeneration
- η_Carnot at ideal limit
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
The Stirling cycle uses 2 isothermal legs and 2 isochoric legs, no adiabatic legs at all. Its efficiency can in principle match the Carnot value if a perfect "regenerator" recycles heat between the isochoric legs. Without an ideal regenerator, does the simple cycle efficiency you measure fall short of the Carnot bound?
Predictions to weigh
- Yes — without a regenerator, this cycle's raw efficiency is below the Carnot limit for the same two reservoir temperatures.
- The efficiency exactly equals the Carnot limit regardless of regeneration.
- The efficiency exceeds the Carnot limit.
Variable roles
What you set:
- Leg number
What you measure:
- Leg's target volume V (m³)
- Work done by gas this leg (J)
How the investigation runs
- Open the stirling-cycle preset and press Reset. 1 mol of argon cycles between 600 K and 300 K using isothermal and isochoric legs only.
- Enable the per-leg work readout and the cycle-efficiency readout.
- For each leg of the cycle (1 through 4), read off the leg's target volume and the work done by the gas during that leg.
Governing equation
Carnot Bound on Cycle Efficiency — η_c = 1 − Tc / Th
No cycle operating between temperatures Tc and Th — Stirling included — can exceed the Carnot efficiency η_c = 1 − Tc/Th. A real (non-regenerated) Stirling cycle falls short of this bound because it dumps unrecovered heat during its isochoric-cooling leg.
What the printable worksheet asks students to work out
- Confirm legs 2 and 4 (isochoric) show W = 0. Sum all 4 legs' work for the net cycle work, and compare the cycle's efficiency reading to the Carnot bound η_c = 1 − 300/600 = 0.5.
- This cycle's raw efficiency (without an ideal regenerator recovering the isochoric legs' heat) stays below 0.5. Explain, using the first law, why heat dumped during the isochoric-cooling leg represents energy the simple engine doesn't recover.
Where this shows up beyond the lab
- A real Stirling engine uses a regenerator — a mesh that stores heat released during isochoric cooling and returns it during isochoric heating. Explain why a perfect regenerator would let this cycle approach the Carnot efficiency even without adiabatic legs.
- Stirling engines are prized for running on any external heat source (solar, waste heat, even temperature differences in space) rather than requiring internal combustion. Why might a closed-cycle engine with external heating be attractive for those applications?
- AP Physics 2 — Unit 9: Thermodynamics
- IB Physics — B.4 Thermodynamics
- General High School Physics — Heat, temperature & gas laws
- NGSS High School Physics — Thermal energy transfer
- Welcome to Stirling Cycle
- Select the chamber
- Press Play
- Regenerative cycle
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
Heat Engines & Carnot Efficiency