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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Name: ____________________   Date: ____________

1.Easy
houseoutside airHPQ̇H​ = 4.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.3 delivers 4.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.3Q̇H = 4.5 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 7.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.5 delivers 7.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.5Q̇H = 7.5 kW
Ẇ = kW
3.Medium
TH​ = 700 °CTL​ = 30 °CEQH​ = 500 kJQL​W = ?

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 30 °C. It takes in 500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 700 °CTL = 30 °CQH = 500 kJ
Wmax = kJ
4.Medium
TH​ = 300 °CTL​ = ?EQH​ = 2900 kJQL​ = 1686 kJW

A reversible (Carnot) heat engine takes in 2900 kJ of heat from a reservoir at 300 °C and rejects 1686 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 300 °CQH = 2900 kJQL = 1686 kJ
TL = °C
5.Hard
TH​ = 1000 °CT0​ = 30 °CTL​ = -30 °CERWQ̇H​ = 100 kWQ̇L​ = ?

A Carnot heat engine receives 100 kW of heat from a source at 1000 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -30 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 1000 °CT0 = 30 °CTL = -30 °CQ̇H = 100 kW
Q̇L = kW
6.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 9 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 2 °CQ̇H = 9 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 1.047 kW
  2. 2. Ẇ = 3 kW
  3. 3. Wmax = 344.2 kJ
  4. 4. TL = 60.07 °C
  5. 5. Q̇L = 308.8 kW
  6. 6. Ẇmin = 0.5526 kW

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