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​ = 1.12 kWẆ = 0.4 kW

A refrigerator removes heat from its cold space at a rate of 1.12 kW while its compressor uses 0.4 kW of power. Find its coefficient of performance COPR.

Q̇L = 1.12 kWẆ = 0.4 kW
COPR =
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 2.56 kWẆ = 0.8 kW

A refrigerator removes heat from its cold space at a rate of 2.56 kW while its compressor uses 0.8 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.56 kWẆ = 0.8 kW
Q̇H = kW
3.Medium
TH​ = 900 °CTL​ = 30 °CEQH​QL​η = 48%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 48%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 30 °Cη = 48%
ηII = %
4.Medium
TH​ = 200 °CTL​ = ?EQH​ = 1100 kJQL​ = 670 kJW

A reversible (Carnot) heat engine takes in 1100 kJ of heat from a reservoir at 200 °C and rejects 670 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 200 °CQH = 1100 kJQL = 670 kJ
TL = °C
5.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 2 °CQ̇H = 13 kW
Ẇmin = kW
6.Hard
500 °CTm​ = ?25 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 500 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 25 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 500 °CTL = 25 °C
Tm = °C

Answer key

  1. 1. COPR = 2.8
  2. 2. Q̇H = 3.36 kW
  3. 3. ηII = 64.73 %
  4. 4. TL = 15.04 °C
  5. 5. Ẇmin = 0.7982 kW
  6. 6. Tm = 207 °C

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