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
kitchencold spaceRQ̇H​ = ?Q̇L​ = 1.14 kWẆ = 0.3 kW

A refrigerator removes heat from its cold space at a rate of 1.14 kW while its compressor uses 0.3 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 1.14 kWẆ = 0.3 kW
Q̇H = kW
2.Easy
houseoutside airHPQ̇H​ = 8.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.6 delivers 8.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.6Q̇H = 8.5 kW
Ẇ = kW
3.Medium
TH​ = 200 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 200 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 550 °CTL​ = 35 °CEQH​QL​η = 34%

A heat engine receives heat from a source at 550 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 34%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 550 °CTL = 35 °Cη = 34%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 5 °CQ̇H = 13 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 10 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 10 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 5 °CQ̇H = 10 kW
COPmax =

Answer key

  1. 1. Q̇H = 1.44 kW
  2. 2. Ẇ = 1.848 kW
  3. 3. ηmax = 39.1 %
  4. 4. ηII = 54.34 %
  5. 5. Ẇmin = 0.7488 kW
  6. 6. COPmax = 17.36

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