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
hot reservoircold reservoirEQH​ = 700 kJQL​ = 420 kJW

A heat engine takes in 700 kJ of heat from a hot reservoir and rejects 420 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 700 kJQL = 420 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 7.02 kWẆ = 1.8 kW

A refrigerator removes heat from its cold space at a rate of 7.02 kW while its compressor uses 1.8 kW of power. Find its coefficient of performance COPR.

Q̇L = 7.02 kWẆ = 1.8 kW
COPR =
3.Medium
TH​ = 750 °CTL​ = 15 °CEQH​QL​η = 50%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 50%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 15 °Cη = 50%
ηII = %
4.Medium
TH​ = 750 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 750 °CTL = 35 °C
ηmax = %
5.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 2 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 25 °CTL​ = 2 °CRQ̇H​Q̇L​ = 0.5 kWẆ = ?

A refrigerator keeps its cold space at 2 °C in a kitchen at 25 °C, removing heat from the cold space at 0.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 2 °CQ̇L = 0.5 kW
Ẇmin = kW

Answer key

  1. 1. η = 40 %
  2. 2. COPR = 3.9
  3. 3. ηII = 69.6 %
  4. 4. ηmax = 69.88 %
  5. 5. Ẇmin = 0.6459 kW
  6. 6. Ẇmin = 0.0418 kW

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