Heat engines & refrigerators worksheet with answers

Free printable Heat engines & refrigerators worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
hot reservoircold reservoirEQH​ = 3000 kJQL​ = 2250 kJW

A heat engine takes in 3000 kJ of heat from a hot reservoir and rejects 2250 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3000 kJQL = 2250 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 16 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.4 delivers 16 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.4Q̇H = 16 kW
Q̇L = kW
3.Medium
TH​ = 325 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 850 °CTL​ = 30 °CEQH​QL​η = 51%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 51%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 30 °Cη = 51%
ηII = %
5.Hard
TH​ = 400 °CTL​ = 30 °CEQH​ = 3800 kJQL​ = 2356 kJW = 1444 kJ

A heat engine takes in 3800 kJ of heat from a reservoir at 400 °C, produces 1444 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 400 °CTL = 30 °CQH = 3800 kJW = 1444 kJ
Sgen = kJ/K
6.Hard
TH​ = 30 °CTL​ = 5 °CRQ̇H​Q̇L​ = 1 kWẆ

A refrigerator keeps its cold space at 5 °C in a kitchen at 30 °C, removing heat from the cold space at 1 kW. Find the highest possible coefficient of performance COPmax.

TH = 30 °CTL = 5 °CQ̇L = 1 kW
COPmax =

Answer key

  1. 1. η = 25 %
  2. 2. Q̇L = 12.36 kW
  3. 3. ηmax = 48.48 %
  4. 4. ηII = 69.85 %
  5. 5. Sgen = 2.127 kJ/K
  6. 6. COPmax = 11.13

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