A heat pump has COP_HP = 4. For every 1 joule of electrical work input, how many joules of heat are delivered to the warm space?
A1 joule — the same as direct electric resistance heating
B3 joules — equal to the heat extracted from the cold source
C4 joules — equal to COP_HP × work input
D5 joules — the sum of work input and heat extracted from the cold source
By definition, COP_HP = Q_H / W, so Q_H = COP_HP × W = 4 × 1 = 4 joules. Energy conservation confirms this: Q_H = Q_C + W, so Q_C = 3 joules were extracted from the cold reservoir. Option A describes resistance heating (COP = 1). Option B is Q_C — the heat removed from outdoors, not what is delivered indoors. Option D (5 joules) would violate energy conservation.
Question 2 Multiple Choice
You leave a refrigerator door wide open in a perfectly sealed room for several hours. The net effect on the room's temperature is:
AThe room cools down, because the refrigerator is constantly removing heat from the air
BThe room temperature stays the same, since the refrigerator just moves heat within the room
CThe room warms up, because the refrigerator's motor continuously adds electrical energy to the room as heat
DThe room first cools, then returns to its original temperature at equilibrium
The refrigerator uses electrical work W to move Q_C from the compartment to the kitchen, depositing Q_H = Q_C + W into the room. With the door open, compartment and room temperatures equalize, but the motor keeps running, continuously injecting W joules of electrical energy into the room as heat. The sealed room warms because Q_H = Q_C + W always exceeds Q_C — the room receives more heat than the refrigerator removes from the air. This follows directly from energy conservation.
Question 3 True / False
A heat pump with COP_HP = 3 can deliver 3 joules of heat per joule of electrical work without violating energy conservation, because it moves thermal energy from a cold source rather than creating it.
TTrue
FFalse
Answer: True
COP > 1 is not magic — the heat pump extracts Q_C = 2 joules from cold outdoor air and adds the 1 joule of work, delivering Q_H = 3 joules. Energy is conserved: 2 (from outdoors) + 1 (electrical) = 3 (delivered). The 'extra' heat comes from the outdoor thermal reservoir, which loses energy in the process. No energy is created; it is relocated from cold to warm with mechanical assistance.
Question 4 True / False
The coefficient of performance of a refrigerator or heat pump cannot exceed 1, because no device can deliver more energy output than it consumes.
TTrue
FFalse
Answer: False
COP can greatly exceed 1, and this does not violate energy conservation. A refrigerator's useful output Q_C can exceed work W because additional energy Q_C comes from the thermal reservoir being cooled. For a heat pump, Q_H = Q_C + W > W always, so COP_HP > 1 always. Real heat pumps routinely achieve COP of 3–5. The first law is satisfied because energy is conserved across the entire system — the cold reservoir loses Q_C.
Question 5 Short Answer
Why can a heat pump deliver more heat energy to a building than the electrical energy it consumes, without violating the first law of thermodynamics?
Think about your answer, then reveal below.
Model answer: A heat pump doesn't create energy — it moves it. The electrical work W drives a thermodynamic cycle that extracts heat Q_C from a cold outdoor source and delivers the combined Q_H = Q_C + W to the building. The 'extra' heat comes from the outdoor thermal reservoir, which loses that energy. Energy is conserved: Q_C (from outdoors) + W (electricity) = Q_H (delivered indoors). The efficiency advantage over resistance heating arises because the device transports existing thermal energy rather than converting electricity directly into heat.
Analogy: a water pump delivers more water to a height than the energy put into the pump — the rest was already there; you paid only for the pumping. Similarly, a heat pump delivers more thermal energy than your electricity bill covers — you paid for the thermodynamic pumping of heat from cold to warm, while the rest came from the outdoor air for free.