The Reversed Carnot Cycle: A Refrigerator
1 · Predict
Running the Carnot cycle backward turns an engine into a refrigerator — net work goes IN instead of coming out. Does the gas still absorb heat from the cold reservoir, like a real fridge pulling heat out of its interior?
- Yes — the reversed cycle absorbs heat from the cold side and dumps more heat into the hot side, using the input work to do it.
- No — reversing the cycle also reverses which reservoir absorbs heat.
- A reversed cycle doesn't exchange heat with either reservoir.
2 · Set Up
- Open the carnot-fridge preset and press Reset. The same 4 legs as carnot-cycle run in reverse order.
- Enable the per-leg work readout, and the cooling/heating COP readouts.
- 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, tracing the legs in order. Compare the direction of travel (clockwise or counterclockwise) to the carnot-cycle experiment's diagram.
4 · Analyze
- Sum your 4 legs' work values — the total (net work done BY the gas) should come out negative, meaning net work must be supplied TO the gas. Compute the cooling COP = Tc/(Th − Tc) = 300/(600−300) = 1.0 and heating COP = Th/(Th − Tc) = 2.0.
- Compare the leg order here to carnot-cycle's leg order. Explain how simply reversing the sequence of the same 4 legs flips the cycle from an engine (net work out) into a refrigerator (net work in).
5 · Extend
- A cooling COP of 1.0 means the fridge moves 1 J of heat out of the cold space for every 1 J of work supplied. A heating COP of 2.0 (heat pump mode) means it delivers 2 J of heat to the warm space per 1 J of work. Explain why COP_heat is always exactly 1 more than COP_cool for the same reservoirs.
- Unlike engine efficiency (always ≤ 1), COP can exceed 1 — that's not a violation of energy conservation. Explain why COP > 1 is possible: the extra energy delivered comes from the reservoir being cooled, not created from nothing.
The Physics Behind This Experiment
Refrigerator Coefficient of Performance
A reversed Carnot cycle's cooling performance is measured by COP_cool = Tc/(Th − Tc): how much heat is removed from the cold space per unit of work supplied. Smaller temperature gaps give better (higher) COP.