Thermodynamics

Carnot cycle

The most efficient cycle: η = 1 − Tc/Th.

Run a Carnot heat engine through isothermal and adiabatic steps on a PV diagram. Track efficiency, heat flow, and entropy changes in a thermodynamics simulation.

Carnot efficiency

The most efficient cycle: η = 1 − Tc/Th.

A Carnot engine operates reversibly between two reservoirs. Each leg is either isothermal (heat exchange at fixed T) or adiabatic (no heat). No real engine can exceed this efficiency because irreversibility wastes useful energy as entropy production.

• η = 1 − T_c/T_h
• Maximum η

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

A Carnot engine carries gas through 4 legs (isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression) back to its starting state. Does the gas's internal energy change over one complete cycle?

Predictions to weigh

• Internal energy increases over the cycle, since the gas does net positive work.
• Internal energy returns to its starting value — zero net change over a closed cycle.
• Internal energy decreases over the cycle.

Variable roles

What you set:

• Leg number

What you measure:

• Leg's target volume V (L)
• Work done by gas this leg (J)

How the investigation runs

1. Open the carnot-cycle preset and press Reset. 1 mol of argon (f = 3) cycles between a 600 K hot reservoir and a 300 K cold reservoir.
2. Enable the per-leg work readout.
3. 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 Efficiency — η_c = 1 − Tc / Th

The maximum possible efficiency of any heat engine operating between a hot reservoir Th and a cold reservoir Tc depends only on their temperature ratio: η_c = 1 − Tc/Th.

What the printable worksheet asks students to work out

• Add up your 4 legs' work values. Compare the total to nR(Th − Tc)·ln(2) (approximately, for this cycle's volume ratios), and compare the cycle's efficiency η = W_net/Qin to the Carnot value η_c = 1 − Tc/Th = 1 − 300/600 = 0.5.
• Two legs have positive work (expansion) and two have negative work (compression). Explain why the *net* work over the full cycle is still positive, making this a heat engine rather than a do-nothing loop.

Where this shows up beyond the lab

• No real engine operating between the same two reservoir temperatures can beat the Carnot efficiency. Explain, using η_c = 1 − Tc/Th, why an engine could reach 100% efficiency only if Tc = 0 K — physically unreachable.
• The Carnot cycle is built entirely from reversible steps (isothermal and adiabatic, both idealized as infinitely slow). Explain why a real engine, which inevitably has friction and finite-speed heat transfer, can never quite reach this ideal efficiency.

• 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

1. Welcome to Carnot Cycle
2. Select the chamber
3. Press Play
4. Maximum efficiency
5. Open the Properties panel
6. You did it!

Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.

Open Interactive Lab →

Download lab sheet →

Heat Engines & Carnot Efficiency