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
houseoutside airHPQ̇H​ = 9 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.2 delivers 9 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.2Q̇H = 9 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 1400 kJQL​ = 910 kJW

A heat engine takes in 1400 kJ of heat from a hot reservoir and rejects 910 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1400 kJQL = 910 kJ
η = %
3.Medium
TH​ = 625 °CTL​ = 5 °CEQH​ = 3400 kJQL​W = ?

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 5 °C. It takes in 3400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 625 °CTL = 5 °CQH = 3400 kJ
Wmax = kJ
4.Medium
TH​ = 450 °CTL​ = 30 °CEQH​ = 3100 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 30 °C. It takes in 3100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 30 °CQH = 3100 kJ
Wmax = kJ
5.Hard
TH​ = 750 °CT0​ = 27 °CTL​ = -25 °CERWQ̇H​ = 150 kWQ̇L​ = ?

A Carnot heat engine receives 150 kW of heat from a source at 750 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -25 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 750 °CT0 = 27 °CTL = -25 °CQ̇H = 150 kW
Q̇L = kW
6.Hard
TH​ = 30 °CTL​ = -20 °CRQ̇H​Q̇L​ = 2.5 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 30 °C, removing heat from the cold space at 2.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -20 °CQ̇L = 2.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 6.857 kW
  2. 2. η = 35 %
  3. 3. Wmax = 2347 kJ
  4. 4. Wmax = 1800 kJ
  5. 5. Q̇L = 505.8 kW
  6. 6. Ẇmin = 0.4938 kW

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