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 = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 30%
Q̇H = MW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 40%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 40%
Q̇H = MW
3.Medium
TH​ = 400 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 400 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 700 °CTL​ = 40 °CEQH​QL​η = 27%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 27%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 40 °Cη = 27%
ηII = %
5.Hard
TH​ = 28 °CTL​ = -18 °CRQ̇H​Q̇L​ = 4.5 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 28 °C, removing heat from the cold space at 4.5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = -18 °CQ̇L = 4.5 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 5 °C outside, delivering 11 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 5 °CQ̇H = 11 kW
COPmax =

Answer key

  1. 1. Q̇H = 2500 MW
  2. 2. Q̇H = 500 MW
  3. 3. ηmax = 56.45 %
  4. 4. ηII = 39.81 %
  5. 5. Ẇmin = 0.8113 kW
  6. 6. COPmax = 18.38

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