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​ = 3900 kJQL​ = 2145 kJW

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2145 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3900 kJQL = 2145 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 2.08 kWẆ = 1.3 kW

A refrigerator removes heat from its cold space at a rate of 2.08 kW while its compressor uses 1.3 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.08 kWẆ = 1.3 kW
Q̇H = kW
3.Medium
TH​ = 300 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 300 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 300 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 500 °CTL​ = 35 °CEQH​QL​η = 30%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 30%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 35 °Cη = 30%
ηII = %
5.Hard
TH​ = 30 °CTL​ = 5 °CRQ̇H​Q̇L​ = 4 kWẆ

A refrigerator keeps its cold space at 5 °C in a kitchen at 30 °C, removing heat from the cold space at 4 kW. Find the highest possible coefficient of performance COPmax.

TH = 30 °CTL = 5 °CQ̇L = 4 kW
COPmax =
6.Hard
TH​ = 25 °CTL​ = 5 °CRQ̇H​Q̇L​ = 0.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °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 = 5 °CQ̇L = 0.5 kW
Ẇmin = kW

Answer key

  1. 1. η = 45 %
  2. 2. Q̇H = 3.38 kW
  3. 3. ηmax = 49.73 %
  4. 4. ηII = 49.88 %
  5. 5. COPmax = 11.13
  6. 6. Ẇmin = 0.03595 kW

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