A Carnot engine operates between a hot reservoir at 1000 K and a cold reservoir, with efficiency 0.4. It absorbs 150 J per cycle. Its entire work output runs a heat pump of coefficient of performance 10 whose hot reservoir is at 300 K. Which statements are correct?
Select all that apply

Question

A Carnot engine operates between a hot reservoir at 1000 K and a cold reservoir, with efficiency 0.4. It absorbs 150 J per cycle. Its entire work output runs a heat pump of coefficient of performance 10 whose hot reservoir is at 300 K. Which statements are correct?

Select all that apply

G1 Physics · Accepted Answer

Engine work: W = ηQ = 0.4 × 150 = 60 J. So A is true. For the Carnot engine, the efficiency relation is η = 1 − (cold-reservoir temperature)/(hot-reservoir temperature). Therefore 0.4 = 1 − (cold-reservoir temperature)/1000, so the cold-reservoir temperature is 600 K. Thus B is true. For the reversible heat pump, COP = (hot-reservoir temperature) / [(hot-reservoir temperature) − (cold-reservoir temperature)]. Hence 10 = 300/[300 − (cold-reservoir temperature)], which gives the cold-reservoir te…