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​ = 2090 kJW

A heat engine takes in 3800 kJ of heat from a hot reservoir and rejects 2090 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3800 kJQL = 2090 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 700 kJQL​ = 560 kJW

A heat engine takes in 700 kJ of heat from a hot reservoir and rejects 560 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 700 kJQL = 560 kJ
η = %
3.Medium
TH​ = 850 °CTL​ = 30 °CEQH​QL​η = 55%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 55%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 30 °Cη = 55%
ηII = %
4.Medium
TH​ = 20 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 6.5 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 6.5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -10 °CTH = 20 °CQ̇L = 6.5 kW
Q̇H = kW
5.Hard
TH​ = 20 °CTL​ = 5 °CHPQ̇H​ = 17.5 kWQ̇L​Ẇ = ?

A heat pump delivers 17.5 kW of heat to a heating system at 20 °C, taking heat from a source at 5 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = 5 °CηII = 60%Q̇H = 17.5 kW
Ẇ = kW
6.Hard
TH​ = 750 °CTL​ = 15 °CEQH​ = 4000 kJQL​ = 2560 kJW = 1440 kJ

A heat engine takes in 4000 kJ of heat from a reservoir at 750 °C, produces 1440 kJ of work and rejects the rest to a reservoir at 15 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 15 °CQH = 4000 kJW = 1440 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 45 %
  2. 2. η = 20 %
  3. 3. ηII = 75.33 %
  4. 4. Q̇H = 7.241 kW
  5. 5. Ẇ = 1.492 kW
  6. 6. Sgen = 4.975 kJ/K

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