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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Name: ____________________   Date: ____________

1.Easy
houseoutside airHPQ̇H​ = 17 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.5 delivers 17 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.5Q̇H = 17 kW
Q̇L = kW
2.Easy
houseoutside airHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.8 delivers 13 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.8Q̇H = 13 kW
Ẇ = kW
3.Medium
TH​ = 800 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 375 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 375 °CTL = 35 °C
ηmax = %
5.Hard
TH​ = 55 °CTL​ = 0 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump delivers 12 kW of heat to a heating system at 55 °C, taking heat from a source at 0 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 0 °CηII = 50%Q̇H = 12 kW
Ẇ = kW
6.Hard
TH​ = 55 °CTL​ = 10 °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 10 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 10 °CηII = 30%Q̇H = 4 kW
Ẇ = kW

Answer key

  1. 1. Q̇L = 12.14 kW
  2. 2. Ẇ = 4.643 kW
  3. 3. ηmax = 73.15 %
  4. 4. ηmax = 52.46 %
  5. 5. Ẇ = 4.023 kW
  6. 6. Ẇ = 1.828 kW

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