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​ = 18 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.3 delivers 18 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.3Q̇H = 18 kW
Q̇L = kW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 7.36 kWẆ = 2.3 kW

A refrigerator removes heat from its cold space at a rate of 7.36 kW while its compressor uses 2.3 kW of power. Find its coefficient of performance COPR.

Q̇L = 7.36 kWẆ = 2.3 kW
COPR =
3.Medium
TH​ = 350 °CTL​ = 20 °CEQH​QL​η = 29%

A heat engine receives heat from a source at 350 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 29%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 350 °CTL = 20 °Cη = 29%
ηII = %
4.Medium
TH​ = 30 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 6 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 6 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = 0 °CTH = 30 °CQ̇L = 6 kW
Q̇H = kW
5.Hard
TH​ = 45 °CTL​ = 5 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump delivers 12 kW of heat to a heating system at 45 °C, taking heat from a source at 5 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = 5 °CηII = 30%Q̇H = 12 kW
Ẇ = kW
6.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 12 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 2 °CQ̇H = 12 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 13.81 kW
  2. 2. COPR = 3.2
  3. 3. ηII = 54.76 %
  4. 4. Q̇H = 6.659 kW
  5. 5. Ẇ = 5.029 kW
  6. 6. Ẇmin = 0.7368 kW

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