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
houseoutside airHPQ̇H​ = 7 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.3 delivers 7 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.3Q̇H = 7 kW
Q̇L = kW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 5 kWẆ = 2.5 kW

A refrigerator removes heat from its cold space at a rate of 5 kW while its compressor uses 2.5 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 5 kWẆ = 2.5 kW
Q̇H = kW
3.Medium
TH​ = 500 °CTL​ = 40 °CEQH​QL​η = 45%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 45%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 40 °Cη = 45%
ηII = %
4.Medium
TH​ = 40 °CTL​ = 2 °CRQ̇H​ = ?Q̇L​ = 10 kWẆ

A reversible refrigerator keeps a cold room at 2 °C by removing 10 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = 2 °CTH = 40 °CQ̇L = 10 kW
Q̇H = kW
5.Hard
900 °CTm​ = ?30 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 900 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 30 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 900 °CTL = 30 °C
Tm = °C
6.Hard
TH​ = 30 °CTL​ = 4 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 4 °CQ̇L = 1.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 4.879 kW
  2. 2. Q̇H = 7.5 kW
  3. 3. ηII = 75.63 %
  4. 4. Q̇H = 11.38 kW
  5. 5. Tm = 323.2 °C
  6. 6. Ẇmin = 0.1407 kW

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