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​ = 1500 kJQL​ = 1200 kJW

A heat engine takes in 1500 kJ of heat from a hot reservoir and rejects 1200 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1500 kJQL = 1200 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 17.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.1 delivers 17.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.1Q̇H = 17.5 kW
Q̇L = kW
3.Medium
TH​ = 300 °CTL​ = 40 °CEQH​QL​η = 18%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 18%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 40 °Cη = 18%
ηII = %
4.Medium
TH​ = 28 °CTL​ = -5 °CRQ̇H​ = ?Q̇L​ = 4 kWẆ

A reversible refrigerator keeps a cold room at -5 °C by removing 4 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -5 °CTH = 28 °CQ̇L = 4 kW
Q̇H = kW
5.Hard
TH​ = 650 °CT0​ = 25 °CTL​ = -30 °CERWQ̇H​ = 190 kWQ̇L​ = ?

A Carnot heat engine receives 190 kW of heat from a source at 650 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -30 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 25 °CTL = -30 °CQ̇H = 190 kW
Q̇L = kW
6.Hard
TH​ = 500 °CT0​ = 27 °CTL​ = -15 °CERWQ̇H​ = 90 kWQ̇L​ = ?

A Carnot heat engine receives 90 kW of heat from a source at 500 °C and rejects heat to the surroundings at 27 °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 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 500 °CT0 = 27 °CTL = -15 °CQ̇H = 90 kW
Q̇L = kW

Answer key

  1. 1. η = 20 %
  2. 2. Q̇L = 11.85 kW
  3. 3. ηII = 39.68 %
  4. 4. Q̇H = 4.492 kW
  5. 5. Q̇L = 568.7 kW
  6. 6. Q̇L = 338.4 kW

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