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​ = 3800 kJQL​ = 2280 kJW

A heat engine takes in 3800 kJ of heat from a hot reservoir and rejects 2280 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3800 kJQL = 2280 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 8.88 kWẆ = 2.4 kW

A refrigerator removes heat from its cold space at a rate of 8.88 kW while its compressor uses 2.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 8.88 kWẆ = 2.4 kW
Q̇H = kW
3.Medium
TH​ = 700 °CTL​ = 30 °CEQH​QL​η = 45%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 45%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 30 °Cη = 45%
ηII = %
4.Medium
TH​ = 625 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 625 °CTL = 40 °C
ηmax = %
5.Hard
TH​ = 45 °CTL​ = 2 °CHPQ̇H​ = 17.5 kWQ̇L​Ẇ = ?

A heat pump delivers 17.5 kW of heat to a heating system at 45 °C, taking heat from a source at 2 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = 2 °CηII = 45%Q̇H = 17.5 kW
Ẇ = kW
6.Hard
TH​ = 600 °CTL​ = 35 °CEQH​ = 3600 kJQL​ = 1728 kJW = 1872 kJ

A heat engine takes in 3600 kJ of heat from a reservoir at 600 °C, produces 1872 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 600 °CTL = 35 °CQH = 3600 kJW = 1872 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 40 %
  2. 2. Q̇H = 11.28 kW
  3. 3. ηII = 65.36 %
  4. 4. ηmax = 65.13 %
  5. 5. Ẇ = 5.256 kW
  6. 6. Sgen = 1.485 kJ/K

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