Heat Engine Lab: Compare Efficiency With the Carnot Limit
Set two reservoir temperatures and an engine’s efficiency. Compare work and rejected heat with the Carnot limit.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 8 minutes.
How does it work?
- Change a control to update the table and diagram.
- Open a preset to compare settings, then try the challenges.
What will you get?
Compare the model’s outputs, explore its presets, and check two challenges.
What does the model assume?
- The engine completes a cycle between two reservoirs with fixed temperatures. Temperatures in kelvin equal temperatures in °C plus 273.15.
- The reversible upper limit is 1 − Tc/Th, using absolute temperatures. A real engine with irreversibility operates below that limit.
- Over a complete cycle, work delivered equals heat supplied minus heat rejected. There is no net change in stored energy.
- An actual efficiency above the Carnot limit violates the second law. Work and rejected heat are not reported for that setting or for an invalid reservoir ordering.
- The reservoirs and energy amounts are illustrative. No particular engine is represented.
Which setup would you like to try?
What can you change?
Range: -200 to 1000 °C.
Range: -200 to 1000 °C.
Range: 100 to 10000 J.
Range: 0 to 100 %.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Hot reservoir temperature | 600.00 | K |
| Cold reservoir temperature | 300.00 | K |
| Carnot efficiency limit | 50.00 | % |
| Work delivered per cycle | 400.00 | J |
| Heat rejected per cycle | 600.00 | J |
| Physical consistency | Within the Carnot limit |
Arrow widths scale with energy. Each arrow also carries its value.
Of 1,000 J supplied, 400 J leaves as work and 600 J as rejected heat.
Can you reach these targets?
Set the hot reservoir to 526.85 °C and the actual efficiency to 40%. Find the cold temperature that gives a Carnot limit of 50%.
- Target: Hot reservoir temperature = 526.85 °C; tolerance 0 °C.
- Target: Actual efficiency = 40 %; tolerance 0 %.
- Target: Carnot efficiency limit = 50 %; tolerance 0.001 %.
- Physical consistency (Within the Carnot limit)
Use reservoirs at 326.85 °C and 26.85 °C with 1000 J of heat input. Set an allowed efficiency that delivers 300 J of work.
- Target: Hot reservoir temperature = 326.85 °C; tolerance 0 °C.
- Target: Cold reservoir temperature = 26.85 °C; tolerance 0 °C.
- Target: Heat supplied per cycle = 1000 J; tolerance 0 J.
- Target: Work delivered per cycle = 300 J; tolerance 0.01 J.
- Physical consistency (Within the Carnot limit)