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​ = 3100 kJQL​ = 2170 kJW

A heat engine takes in 3100 kJ of heat from a hot reservoir and rejects 2170 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3100 kJQL = 2170 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 2 kWẆ = 0.5 kW

A refrigerator removes heat from its cold space at a rate of 2 kW while its compressor uses 0.5 kW of power. Find its coefficient of performance COPR.

Q̇L = 2 kWẆ = 0.5 kW
COPR =
3.Medium
TH​ = 20 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 2.5 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 2.5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = 0 °CTH = 20 °CQ̇L = 2.5 kW
Q̇H = kW
4.Medium
TH​ = 725 °CTL​ = 35 °CEQH​ = 4800 kJQL​W = ?

A heat engine works between a hot reservoir at 725 °C and a cold reservoir at 35 °C. It takes in 4800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 725 °CTL = 35 °CQH = 4800 kJ
Wmax = kJ
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -10 °CQ̇H = 13 kW
Ẇmin = kW
6.Hard
TH​ = 45 °CTL​ = -10 °CHPQ̇H​ = 4.5 kWQ̇L​Ẇ = ?

A heat pump delivers 4.5 kW of heat to a heating system at 45 °C, taking heat from a source at -10 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = -10 °CηII = 60%Q̇H = 4.5 kW
Ẇ = kW

Answer key

  1. 1. η = 30 %
  2. 2. COPR = 4
  3. 3. Q̇H = 2.683 kW
  4. 4. Wmax = 3318 kJ
  5. 5. Ẇmin = 1.37 kW
  6. 6. Ẇ = 1.297 kW

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