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​ = 11.76 kWẆ = 2.8 kW

A refrigerator removes heat from its cold space at a rate of 11.76 kW while its compressor uses 2.8 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 11.76 kWẆ = 2.8 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 4200 kJQL​ = 3360 kJW

A heat engine takes in 4200 kJ of heat from a hot reservoir and rejects 3360 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4200 kJQL = 3360 kJ
η = %
3.Medium
TH​ = 450 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 450 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 500 °CTL​ = 10 °CEQH​QL​η = 32%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 32%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 10 °Cη = 32%
ηII = %
5.Hard
TH​ = 32 °CTL​ = -25 °CRQ̇H​Q̇L​ = 3.5 kWẆ

A refrigerator keeps its cold space at -25 °C in a kitchen at 32 °C, removing heat from the cold space at 3.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = -25 °CQ̇L = 3.5 kW
COPmax =
6.Hard
TH​ = 25 °CTL​ = 5 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 25 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 5 °CQ̇L = 3.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 14.56 kW
  2. 2. η = 20 %
  3. 3. ηmax = 59.46 %
  4. 4. ηII = 50.49 %
  5. 5. COPmax = 4.354
  6. 6. Ẇmin = 0.2517 kW

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