First consider a Carnot engine that operates between a hot reservoir at 58°C and a cold reservoir at - 17°C. In running 24 minutes, this engine absorbs 590 J of heat from the hot reservoir. 1) How much heat does it expel to the cold reservoir?

Given that,

Hot reservoir temperature is

TH = 58°C

TH = 58 + 273 = 331 K

Cold reservoir temperature

TC = - 17°C

TC = - 17°C + 273 = 256K

In 24minutes 590 J of heat was removed from hot reservoir

t = 24mins

t = 24 * 60 = 1440 seconds

Then,

Power is given as

P = E / t

P = 590 / 1440

P = 0.41 W

Since this removed from the hot reservoir, then, QH = 0.41W

We want to find heat expelled to the cold reservoir QX

Efficiency is given as

η = 1 - TH/TC = 1 - QH/QC

1 - TH/TC = 1 - QH/QC

TH/TC = QH/QC

Make QC subject of formula

QC = QH * TC / TH

QC = 0.41 * 256 / 331

QC = 0.317 W