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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 45%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 45%
Q̇H = MW
2.Easy
houseoutside airHPQ̇H​ = 16 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4 delivers 16 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4Q̇H = 16 kW
Q̇L = kW
3.Medium
TH​ = 40 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 7 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 7 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 kW
Q̇H = kW
4.Medium
TH​ = 500 °CTL​ = 30 °CEQH​QL​η = 33%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 33%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 30 °Cη = 33%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 15.5 kWQ̇L​Ẇ = ?

A heat pump delivers 15.5 kW of heat to a heating system at 21 °C, taking heat from a source at 5 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = 5 °CηII = 35%Q̇H = 15.5 kW
Ẇ = kW
6.Hard
TH​ = 550 °CT0​ = 30 °CTL​ = -15 °CERWQ̇H​ = 160 kWQ̇L​ = ?

A Carnot heat engine receives 160 kW of heat from a source at 550 °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 = 550 °CT0 = 30 °CTL = -15 °CQ̇H = 160 kW
Q̇L = kW

Answer key

  1. 1. Q̇H = 444.4 MW
  2. 2. Q̇L = 12 kW
  3. 3. Q̇H = 8.591 kW
  4. 4. ηII = 54.28 %
  5. 5. Ẇ = 2.409 kW
  6. 6. Q̇L = 579.8 kW

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