The Memory Trick
💡 Engine Forward, Refrigerator in Reverse
A heat engine takes heat from a hot reservoir and converts some of it to useful work, rejecting the rest to a cold reservoir. A refrigerator (or heat pump) runs this exact cycle in reverse: it uses work input to forcibly move heat from a cold reservoir to a hot one — something that would never happen spontaneously, per the Second Law, without that work input.
Why It Works
Performance for a refrigerator/heat pump is measured by Coefficient of Performance (COP) rather than efficiency, because these devices aren't converting heat to work — they're using work to MOVE heat, and can legitimately move far more heat energy than the work energy put in, since they're relocating existing heat rather than creating new energy.
Step by Step
Refrigerators and Heat Pumps
1
Refrigerator COP — moving heat OUT of the cold space
COP_refrigerator = Qc/W — the ratio of heat removed from the cold space to the work required to remove it. At the Carnot limit, COP_refrig = Tc/(Th−Tc).
A refrigerator's job is to keep its interior cold, so its useful output is Qc (heat removed from inside), measured against the work (electricity) it consumes.
2
Heat pump COP — moving heat INTO the hot space
COP_heat pump = Qh/W — the ratio of heat delivered to the hot space to the work required. At the Carnot limit, COP_HP = Th/(Th−Tc). Note Qh = Qc + W, so COP_HP is always exactly 1 greater than COP_refrig for the same cycle.
A heat pump's job is to warm a space, so its useful output is Qh (heat delivered), even though it's running the exact same physical cycle as a refrigerator.
3
Why heat pumps can exceed 100% 'efficiency'
A heat pump can deliver MORE heat energy (Qh) than the work energy (W) it consumes — this isn't a violation of energy conservation, because it's not creating energy, just relocating existing heat from the cold reservoir using the work as a 'lever.'
A heat pump with COP_HP = 3 delivers 3 units of heat energy to a room for every 1 unit of electrical work consumed — 2 of those 3 units came from the outside cold air, not from the electricity itself.
🏥 Worked Example
A refrigerator removes 200 J of heat from its interior for every 50 J of work (electricity) it consumes. What is its Coefficient of Performance, and how much heat does it reject to the room per cycle?
1
Calculate COP_refrigerator: COP = Qc/W = 200/50 = 4.
2
Find heat rejected to the hot side (the room): Qh = Qc + W = 200 + 50 = 250 J.
3
Interpret: the refrigerator moves 200 J out of its interior using only 50 J of work, then dumps the total 250 J (the removed heat PLUS the work energy) into the room — which is exactly why the space behind a running refrigerator always feels warm.
📌 Exam Application
Exams test correctly calculating COP for both refrigerators and heat pumps, applying Qh = Qc + W (energy conservation for the reversed cycle), and explaining why COP values above 1 don't violate energy conservation.
⚠️ Most Common Heat Engines and Refrigerators Mistakes
The most common trap is confusing refrigerator COP with heat pump COP for the same physical device — they're numerically different (COP_HP = COP_refrig + 1) because they measure the ratio against different useful outputs (heat removed from cold side vs. heat delivered to hot side), even though it's the exact same physical cycle.
✓ Quick Self-Test
1) How does a refrigerator relate to a heat engine? It runs the same cycle in reverse, using work input to move heat from cold to hot instead of converting heat to work. 2) Write the formula for refrigerator Coefficient of Performance. COP_refrigerator = Qc/W. 3) Write the formula for heat pump Coefficient of Performance, and state its relationship to refrigerator COP for the same cycle. COP_heat pump = Qh/W; it's always exactly 1 greater than COP_refrigerator for the same cycle (since Qh = Qc + W). 4) Can a heat pump's COP exceed 1 (100%)? Yes — this doesn't violate energy conservation, since the heat pump is moving existing heat energy using work as a lever, not creating new energy. 5) Why does the area behind a running refrigerator feel warm? The refrigerator rejects both the heat removed from its interior (Qc) AND the work energy consumed (W) into the surrounding room as Qh = Qc + W.