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​ = 2600 kJQL​ = 1560 kJW

A heat engine takes in 2600 kJ of heat from a hot reservoir and rejects 1560 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2600 kJQL = 1560 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 4.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.1 delivers 4.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.1Q̇H = 4.5 kW
Q̇L = kW
3.Medium
TH​ = 300 °CTL​ = 5 °CEQH​ = 3600 kJQL​W = ?

A heat engine works between a hot reservoir at 300 °C and a cold reservoir at 5 °C. It takes in 3600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 300 °CTL = 5 °CQH = 3600 kJ
Wmax = kJ
4.Medium
TH​ = 700 °CTL​ = 40 °CEQH​QL​η = 41%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 41%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 40 °Cη = 41%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 7 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 7 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 750 °CT0​ = 20 °CTL​ = -20 °CERWQ̇H​ = 180 kWQ̇L​ = ?

A Carnot heat engine receives 180 kW of heat from a source at 750 °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 -20 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 750 °CT0 = 20 °CTL = -20 °CQ̇H = 180 kW
Q̇L = kW

Answer key

  1. 1. η = 40 %
  2. 2. Q̇L = 3.402 kW
  3. 3. Wmax = 1853 kJ
  4. 4. ηII = 60.45 %
  5. 5. Ẇmin = 0.4759 kW
  6. 6. Q̇L = 812.8 kW

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