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​ = 800 kJQL​ = 600 kJW

A heat engine takes in 800 kJ of heat from a hot reservoir and rejects 600 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 800 kJQL = 600 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 5.27 kWẆ = 1.7 kW

A refrigerator removes heat from its cold space at a rate of 5.27 kW while its compressor uses 1.7 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 5.27 kWẆ = 1.7 kW
Q̇H = kW
3.Medium
TH​ = 375 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 375 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 700 °CTL​ = 40 °CEQH​QL​η = 41%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 41%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 40 °Cη = 41%
ηII = %
5.Hard
TH​ = 850 °CT0​ = 25 °CTL​ = -10 °CERWQ̇H​ = 140 kWQ̇L​ = ?

A Carnot heat engine receives 140 kW of heat from a source at 850 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -10 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 850 °CT0 = 25 °CTL = -10 °CQ̇H = 140 kW
Q̇L = kW
6.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 6 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 6 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = -10 °CQ̇H = 6 kW
COPmax =

Answer key

  1. 1. η = 25 %
  2. 2. Q̇H = 6.97 kW
  3. 3. ηmax = 54.77 %
  4. 4. ηII = 60.45 %
  5. 5. Q̇L = 773.2 kW
  6. 6. COPmax = 9.223

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