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​ = 3200 kJQL​ = 2240 kJW

A heat engine takes in 3200 kJ of heat from a hot reservoir and rejects 2240 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3200 kJQL = 2240 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 2.89 kWẆ = 1.7 kW

A refrigerator removes heat from its cold space at a rate of 2.89 kW while its compressor uses 1.7 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.89 kWẆ = 1.7 kW
COPR =
3.Medium
TH​ = 28 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 8 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 8 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = 0 °CTH = 28 °CQ̇L = 8 kW
Q̇H = kW
4.Medium
TH​ = 375 °CTL​ = 5 °CEQH​ = 2500 kJQL​W = ?

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 5 °C. It takes in 2500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 375 °CTL = 5 °CQH = 2500 kJ
Wmax = kJ
5.Hard
TH​ = 650 °CTL​ = 20 °CEQH​ = 500 kJQL​ = 330 kJW = 170 kJ

A heat engine takes in 500 kJ of heat from a reservoir at 650 °C, produces 170 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 650 °CTL = 20 °CQH = 500 kJW = 170 kJ
Sgen = kJ/K
6.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -10 °CQ̇H = 14 kW
Ẇmin = kW

Answer key

  1. 1. η = 30 %
  2. 2. COPR = 1.7
  3. 3. Q̇H = 8.82 kW
  4. 4. Wmax = 1427 kJ
  5. 5. Sgen = 0.5841 kJ/K
  6. 6. Ẇmin = 1.518 kW

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