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​ = 6.6 kWẆ = 2.2 kW

A refrigerator removes heat from its cold space at a rate of 6.6 kW while its compressor uses 2.2 kW of power. Find its coefficient of performance COPR.

Q̇L = 6.6 kWẆ = 2.2 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 33%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 300 MWη = 33%
Q̇L = MW
3.Medium
TH​ = 650 °CTL​ = 20 °CEQH​ = 500 kJQL​W = ?

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 20 °C. It takes in 500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 650 °CTL = 20 °CQH = 500 kJ
Wmax = kJ
4.Medium
TH​ = 700 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 700 °CTL = 35 °C
ηmax = %
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 4 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 7 °CQ̇H = 4 kW
Ẇmin = kW
6.Hard
TH​ = 1000 °CT0​ = 20 °CTL​ = -10 °CERWQ̇H​ = 150 kWQ̇L​ = ?

A Carnot heat engine receives 150 kW of heat from a source at 1000 °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 -10 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 1000 °CT0 = 20 °CTL = -10 °CQ̇H = 150 kW
Q̇L = kW

Answer key

  1. 1. COPR = 3
  2. 2. Q̇L = 609.1 MW
  3. 3. Wmax = 341.2 kJ
  4. 4. ηmax = 68.33 %
  5. 5. Ẇmin = 0.2033 kW
  6. 6. Q̇L = 1013 kW

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