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​ = 3100 kJQL​ = 2325 kJW

A heat engine takes in 3100 kJ of heat from a hot reservoir and rejects 2325 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3100 kJQL = 2325 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 1900 kJQL​ = 1140 kJW = ?

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1140 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1900 kJQL = 1140 kJ
W = kJ
3.Medium
TH​ = 800 °CTL​ = 25 °CEQH​QL​η = 54%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 54%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 25 °Cη = 54%
ηII = %
4.Medium
TH​ = 850 °CTL​ = 30 °CEQH​QL​η = 44%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 44%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 30 °Cη = 44%
ηII = %
5.Hard
TH​ = 550 °CT0​ = 30 °CTL​ = -25 °CERWQ̇H​ = 140 kWQ̇L​ = ?

A Carnot heat engine receives 140 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 -25 °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 = -25 °CQ̇H = 140 kW
Q̇L = kW
6.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -10 °CQ̇H = 5 kW
Ẇmin = kW

Answer key

  1. 1. η = 25 %
  2. 2. W = 760 kJ
  3. 3. ηII = 74.77 %
  4. 4. ηII = 60.27 %
  5. 5. Q̇L = 399 kW
  6. 6. Ẇmin = 0.5269 kW

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