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
hot reservoircold reservoirEQH​ = 700 kJQL​ = 455 kJW

A heat engine takes in 700 kJ of heat from a hot reservoir and rejects 455 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 700 kJQL = 455 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 0.76 kWẆ = 0.4 kW

A refrigerator removes heat from its cold space at a rate of 0.76 kW while its compressor uses 0.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 0.76 kWẆ = 0.4 kW
Q̇H = kW
3.Medium
TH​ = 500 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 500 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 400 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 400 °CTL = 30 °C
ηmax = %
5.Hard
TH​ = 55 °CTL​ = -10 °CHPQ̇H​ = 7.5 kWQ̇L​Ẇ = ?

A heat pump delivers 7.5 kW of heat to a heating system at 55 °C, taking heat from a source at -10 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = -10 °CηII = 50%Q̇H = 7.5 kW
Ẇ = kW
6.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump delivers 8 kW of heat to a heating system at 21 °C, taking heat from a source at -10 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -10 °CηII = 35%Q̇H = 8 kW
Ẇ = kW

Answer key

  1. 1. η = 35 %
  2. 2. Q̇H = 1.16 kW
  3. 3. ηmax = 60.79 %
  4. 4. ηmax = 54.97 %
  5. 5. Ẇ = 2.971 kW
  6. 6. Ẇ = 2.409 kW

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