The Carnot Cycle: Maximum Possible Engine Efficiency

1 · Predict

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?

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

2 · Set Up

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.

3 · Collect Data

Sketch the P-V diagram for all 4 legs, marking whether each leg is isothermal or adiabatic and whether the gas does positive or negative work.

4 · Analyze

1. 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.
2. 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.

5 · Extend

1. 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.
2. 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.

The Physics Behind This Experiment

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