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
kitchencold spaceRQ̇H​ = ?Q̇L​ = 2.89 kWẆ = 1.7 kW

A refrigerator removes heat from its cold space at a rate of 2.89 kW while its compressor uses 1.7 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.89 kWẆ = 1.7 kW
Q̇H = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 25%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 25%
Q̇H = MW
3.Medium
TH​ = 750 °CTL​ = 40 °CEQH​QL​η = 49%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 49%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 40 °Cη = 49%
ηII = %
4.Medium
TH​ = 725 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 725 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 725 °CTL = 10 °C
ηmax = %
5.Hard
TH​ = 30 °CTL​ = -25 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 30 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -25 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 4 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 4 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = -10 °CQ̇H = 4 kW
COPmax =

Answer key

  1. 1. Q̇H = 4.59 kW
  2. 2. Q̇H = 3000 MW
  3. 3. ηII = 70.61 %
  4. 4. ηmax = 71.63 %
  5. 5. Ẇmin = 0.4433 kW
  6. 6. COPmax = 9.223

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