The Stirling Cycle: Isothermal Legs with Regeneration
1 · Predict
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?
- 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.
2 · Set Up
- 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.
3 · Collect Data
| Leg number | Leg's target volume V (m³) | Work done by gas this leg (J) |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 |
Sketch the P-V diagram for all 4 legs, marking the 2 isothermal (curved) and 2 isochoric (vertical) segments.
4 · Analyze
- 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.
5 · Extend
- 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?
The Physics Behind This Experiment
Carnot Bound on Cycle Efficiency
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.