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​ = 11.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.8 delivers 11.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.8Q̇H = 11.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 1100 kJQL​ = 605 kJW

A heat engine takes in 1100 kJ of heat from a hot reservoir and rejects 605 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1100 kJQL = 605 kJ
η = %
3.Medium
TH​ = 900 °CTL​ = 10 °CEQH​QL​η = 38%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 38%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 10 °Cη = 38%
ηII = %
4.Medium
TH​ = 300 °CTL​ = 25 °CEQH​QL​η = 26%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 26%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 25 °Cη = 26%
ηII = %
5.Hard
TH​ = 35 °CTL​ = 0 °CHPQ̇H​ = 4.5 kWQ̇L​Ẇ = ?

A heat pump delivers 4.5 kW of heat to a heating system at 35 °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 = 35 °CTL = 0 °CηII = 30%Q̇H = 4.5 kW
Ẇ = kW
6.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 7 °CQ̇H = 7 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 9.104 kW
  2. 2. η = 45 %
  3. 3. ηII = 50.09 %
  4. 4. ηII = 54.19 %
  5. 5. Ẇ = 1.704 kW
  6. 6. Ẇmin = 0.3104 kW

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