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​ = 4300 kJQL​ = 2795 kJW

A heat engine takes in 4300 kJ of heat from a hot reservoir and rejects 2795 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4300 kJQL = 2795 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 1000 kJQL​ = 650 kJW

A heat engine takes in 1000 kJ of heat from a hot reservoir and rejects 650 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1000 kJQL = 650 kJ
η = %
3.Medium
TH​ = 250 °CTL​ = ?EQH​ = 1200 kJQL​ = 672 kJW

A reversible (Carnot) heat engine takes in 1200 kJ of heat from a reservoir at 250 °C and rejects 672 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 250 °CQH = 1200 kJQL = 672 kJ
TL = °C
4.Medium
TH​ = 550 °CTL​ = 15 °CEQH​QL​η = 49%

A heat engine receives heat from a source at 550 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 49%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 550 °CTL = 15 °Cη = 49%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 9 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 7 °CQ̇H = 9 kW
Ẇmin = kW
6.Hard
TH​ = 700 °CT0​ = 20 °CTL​ = 0 °CERWQ̇H​ = 150 kWQ̇L​ = ?

A Carnot heat engine receives 150 kW of heat from a source at 700 °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 0 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 700 °CT0 = 20 °CTL = 0 °CQ̇H = 150 kW
Q̇L = kW

Answer key

  1. 1. η = 35 %
  2. 2. η = 35 %
  3. 3. TL = 19.81 °C
  4. 4. ηII = 75.39 %
  5. 5. Ẇmin = 0.4574 kW
  6. 6. Q̇L = 1432 kW

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