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 temperature as 270 K.

Thus C is true.

Heat delivered to the hot reservoir:

Q = COP × W = 10 × 60 = 600 J,

not 540 J. Hence D is false.

Correct options: A, B, C.