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​ = 10.75 kWẆ = 2.5 kW

A refrigerator removes heat from its cold space at a rate of 10.75 kW while its compressor uses 2.5 kW of power. Find its coefficient of performance COPR.

Q̇L = 10.75 kWẆ = 2.5 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 42%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 42%
Q̇H = MW
3.Medium
TH​ = 550 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 550 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 700 °CTL​ = 10 °CEQH​QL​η = 46%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 46%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 10 °Cη = 46%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 5 °CQ̇H = 8 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 5 kW
Ẇmin = kW

Answer key

  1. 1. COPR = 4.3
  2. 2. Q̇H = 476.2 MW
  3. 3. ηmax = 66.21 %
  4. 4. ηII = 64.88 %
  5. 5. Ẇmin = 0.4608 kW
  6. 6. Ẇmin = 0.3388 kW

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