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​ = 3600 kJQL​ = 2880 kJW = ?

A heat engine takes in 3600 kJ of heat from a hot reservoir and rejects 2880 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3600 kJQL = 2880 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4100 kJQL​ = 3075 kJW

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 3075 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4100 kJQL = 3075 kJ
η = %
3.Medium
TH​ = 600 °CTL​ = 20 °CEQH​QL​η = 27%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 27%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 20 °Cη = 27%
ηII = %
4.Medium
TH​ = 725 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 725 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 725 °CTL = 40 °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​ = 850 °CT0​ = 27 °CTL​ = -15 °CERWQ̇H​ = 20 kWQ̇L​ = ?

A Carnot heat engine receives 20 kW of heat from a source at 850 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 850 °CT0 = 27 °CTL = -15 °CQ̇H = 20 kW
Q̇L = kW

Answer key

  1. 1. W = 720 kJ
  2. 2. η = 25 %
  3. 3. ηII = 40.65 %
  4. 4. ηmax = 68.63 %
  5. 5. Ẇmin = 0.2033 kW
  6. 6. Q̇L = 90.08 kW

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