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​ = 15.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.2 delivers 15.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.2Q̇H = 15.5 kW
Ẇ = kW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 12.3 kWẆ = 3 kW

A refrigerator removes heat from its cold space at a rate of 12.3 kW while its compressor uses 3 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 12.3 kWẆ = 3 kW
Q̇H = kW
3.Medium
TH​ = 300 °CTL​ = 40 °CEQH​ = 1300 kJQL​W = ?

A heat engine works between a hot reservoir at 300 °C and a cold reservoir at 40 °C. It takes in 1300 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 300 °CTL = 40 °CQH = 1300 kJ
Wmax = kJ
4.Medium
TH​ = 375 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 375 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 12 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 7 °CQ̇H = 12 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -10 °CQ̇H = 15 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 3.69 kW
  2. 2. Q̇H = 15.3 kW
  3. 3. Wmax = 589.7 kJ
  4. 4. ηmax = 57.09 %
  5. 5. Ẇmin = 0.6099 kW
  6. 6. Ẇmin = 1.626 kW

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