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​ = 0.9 kWẆ = 0.6 kW

A refrigerator removes heat from its cold space at a rate of 0.9 kW while its compressor uses 0.6 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 0.9 kWẆ = 0.6 kW
Q̇H = kW
2.Easy
houseoutside airHPQ̇H​ = 5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.3 delivers 5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.3Q̇H = 5 kW
Q̇L = kW
3.Medium
TH​ = 35 °CTL​ = -5 °CRQ̇H​ = ?Q̇L​ = 10 kWẆ

A reversible refrigerator keeps a cold room at -5 °C by removing 10 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 = 10 kW
Q̇H = kW
4.Medium
TH​ = 550 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 550 °CTL = 30 °C
ηmax = %
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump delivers 19.5 kW of heat to a heating system at 22 °C, taking heat from a source at 7 °C. Its actual COP is 40% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 7 °CηII = 40%Q̇H = 19.5 kW
Ẇ = kW
6.Hard
TH​ = 55 °CTL​ = 0 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump delivers 4 kW of heat to a heating system at 55 °C, taking heat from a source at 0 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 0 °CηII = 30%Q̇H = 4 kW
Ẇ = kW

Answer key

  1. 1. Q̇H = 1.5 kW
  2. 2. Q̇L = 3.837 kW
  3. 3. Q̇H = 11.49 kW
  4. 4. ηmax = 63.17 %
  5. 5. Ẇ = 2.478 kW
  6. 6. Ẇ = 2.235 kW

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