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
kitchencold spaceRQ̇H​Q̇L​ = 3.2 kWẆ = 0.8 kW

A refrigerator removes heat from its cold space at a rate of 3.2 kW while its compressor uses 0.8 kW of power. Find its coefficient of performance COPR.

Q̇L = 3.2 kWẆ = 0.8 kW
COPR =
2.Easy
houseoutside airHPQ̇H​ = 17.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.3 delivers 17.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.3Q̇H = 17.5 kW
Ẇ = kW
3.Medium
TH​ = 40 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 7.5 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 7.5 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 40 °CQ̇L = 7.5 kW
Q̇H = kW
4.Medium
TH​ = 750 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 750 °CTL = 20 °C
ηmax = %
5.Hard
TH​ = 850 °CT0​ = 30 °CTL​ = -15 °CERWQ̇H​ = 70 kWQ̇L​ = ?

A Carnot heat engine receives 70 kW of heat from a source at 850 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 850 °CT0 = 30 °CTL = -15 °CQ̇H = 70 kW
Q̇L = kW
6.Hard
TH​ = 400 °CT0​ = 20 °CTL​ = -25 °CERWQ̇H​ = 180 kWQ̇L​ = ?

A Carnot heat engine receives 180 kW of heat from a source at 400 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -25 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 400 °CT0 = 20 °CTL = -25 °CQ̇H = 180 kW
Q̇L = kW

Answer key

  1. 1. COPR = 4
  2. 2. Ẇ = 5.303 kW
  3. 3. Q̇H = 9.205 kW
  4. 4. ηmax = 71.35 %
  5. 5. Q̇L = 293.2 kW
  6. 6. Q̇L = 560.3 kW

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