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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 30%
Q̇H = MW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 2.15 kWẆ = 0.5 kW

A refrigerator removes heat from its cold space at a rate of 2.15 kW while its compressor uses 0.5 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.15 kWẆ = 0.5 kW
COPR =
3.Medium
TH​ = 325 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 500 °CTL​ = 15 °CEQH​QL​η = 31%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 31%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 15 °Cη = 31%
ηII = %
5.Hard
TH​ = 22 °CTL​ = -5 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -5 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -5 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 28 °CTL​ = 5 °CRQ̇H​Q̇L​ = 3 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 28 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = 5 °CQ̇L = 3 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 2000 MW
  2. 2. COPR = 4.3
  3. 3. ηmax = 51.83 %
  4. 4. ηII = 49.42 %
  5. 5. Ẇmin = 0.9148 kW
  6. 6. Ẇmin = 0.2481 kW

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