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​ = 2700 kJQL​ = 1485 kJW

A heat engine takes in 2700 kJ of heat from a hot reservoir and rejects 1485 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2700 kJQL = 1485 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 1.64 kWẆ = 0.4 kW

A refrigerator removes heat from its cold space at a rate of 1.64 kW while its compressor uses 0.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 1.64 kWẆ = 0.4 kW
Q̇H = kW
3.Medium
TH​ = 525 °CTL​ = ?EQH​ = 1000 kJQL​ = 417 kJW

A reversible (Carnot) heat engine takes in 1000 kJ of heat from a reservoir at 525 °C and rejects 417 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 525 °CQH = 1000 kJQL = 417 kJ
TL = °C
4.Medium
TH​ = 425 °CTL​ = 15 °CEQH​ = 2100 kJQL​W = ?

A heat engine works between a hot reservoir at 425 °C and a cold reservoir at 15 °C. It takes in 2100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 425 °CTL = 15 °CQH = 2100 kJ
Wmax = kJ
5.Hard
TH​ = 750 °CT0​ = 20 °CTL​ = 0 °CERWQ̇H​ = 40 kWQ̇L​ = ?

A Carnot heat engine receives 40 kW of heat from a source at 750 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at 0 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 750 °CT0 = 20 °CTL = 0 °CQ̇H = 40 kW
Q̇L = kW
6.Hard
TH​ = 20 °CTL​ = -5 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -5 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -5 °CQ̇H = 15 kW
Ẇmin = kW

Answer key

  1. 1. η = 45 %
  2. 2. Q̇H = 2.04 kW
  3. 3. TL = 59.68 °C
  4. 4. Wmax = 1233 kJ
  5. 5. Q̇L = 389.8 kW
  6. 6. Ẇmin = 1.279 kW

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