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​ = 14.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.7 delivers 14.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.7Q̇H = 14.5 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.7 delivers 6 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.7Q̇H = 6 kW
Ẇ = kW
3.Medium
TH​ = 25 °CTL​ = 2 °CRQ̇H​ = ?Q̇L​ = 5.5 kWẆ

A reversible refrigerator keeps a cold room at 2 °C by removing 5.5 kW of heat, and rejects heat to the surroundings at 25 °C. Find the rate Q̇H at which it rejects heat.

TL = 2 °CTH = 25 °CQ̇L = 5.5 kW
Q̇H = kW
4.Medium
TH​ = 850 °CTL​ = 20 °CEQH​QL​η = 55%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 55%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 20 °Cη = 55%
ηII = %
5.Hard
TH​ = 32 °CTL​ = -20 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 32 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -20 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 2.5 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 2.5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -10 °CQ̇L = 2.5 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 3.085 kW
  2. 2. Ẇ = 2.222 kW
  3. 3. Q̇H = 5.96 kW
  4. 4. ηII = 74.43 %
  5. 5. Ẇmin = 0.4108 kW
  6. 6. Ẇmin = 0.399 kW

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