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​ = 15 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.4 delivers 15 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.4Q̇H = 15 kW
Ẇ = kW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 0.38 kWẆ = 0.2 kW

A refrigerator removes heat from its cold space at a rate of 0.38 kW while its compressor uses 0.2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 0.38 kWẆ = 0.2 kW
Q̇H = kW
3.Medium
TH​ = 30 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 1.5 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 1.5 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = -10 °CTH = 30 °CQ̇L = 1.5 kW
Q̇H = kW
4.Medium
TH​ = 35 °CTL​ = -5 °CRQ̇H​ = ?Q̇L​ = 5 kWẆ

A reversible refrigerator keeps a cold room at -5 °C by removing 5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -5 °CTH = 35 °CQ̇L = 5 kW
Q̇H = kW
5.Hard
TH​ = 35 °CTL​ = 5 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 35 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = 5 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 11 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 5 °CQ̇H = 11 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 3.409 kW
  2. 2. Q̇H = 0.58 kW
  3. 3. Q̇H = 1.728 kW
  4. 4. Q̇H = 5.746 kW
  5. 5. Ẇmin = 0.2157 kW
  6. 6. Ẇmin = 0.6336 kW

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