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
houseoutside airHPQ̇H​ = 17 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.5 delivers 17 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.5Q̇H = 17 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 16.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.6 delivers 16.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.6Q̇H = 16.5 kW
Q̇L = kW
3.Medium
TH​ = 700 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 700 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 300 °CTL​ = 30 °CEQH​QL​η = 28%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 28%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 30 °Cη = 28%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 2 °CQ̇H = 5 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 6 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 6 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = -10 °CQ̇H = 6 kW
COPmax =

Answer key

  1. 1. Ẇ = 6.8 kW
  2. 2. Q̇L = 12.91 kW
  3. 3. ηmax = 71.42 %
  4. 4. ηII = 59.44 %
  5. 5. Ẇmin = 0.323 kW
  6. 6. COPmax = 9.489

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