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
houseoutside airHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.7 delivers 11 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.7Q̇H = 11 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.8 delivers 10 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.8Q̇H = 10 kW
Ẇ = kW
3.Medium
TH​ = 800 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 650 °CTL​ = 40 °CEQH​QL​η = 36%

A heat engine receives heat from a source at 650 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 36%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 650 °CTL = 40 °Cη = 36%
ηII = %
5.Hard
TH​ = 25 °CTL​ = -20 °CRQ̇H​Q̇L​ = 4.5 kWẆ

A refrigerator keeps its cold space at -20 °C in a kitchen at 25 °C, removing heat from the cold space at 4.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 25 °CTL = -20 °CQ̇L = 4.5 kW
COPmax =
6.Hard
TH​ = 600 °CT0​ = 30 °CTL​ = -25 °CERWQ̇H​ = 50 kWQ̇L​ = ?

A Carnot heat engine receives 50 kW of heat from a source at 600 °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 = 600 °CT0 = 30 °CTL = -25 °CQ̇H = 50 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 2.973 kW
  2. 2. Ẇ = 2.083 kW
  3. 3. ηmax = 73.15 %
  4. 4. ηII = 54.48 %
  5. 5. COPmax = 5.626
  6. 6. Q̇L = 147.3 kW

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