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​ = 16 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.8 delivers 16 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.8Q̇H = 16 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.9 delivers 10 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.9Q̇H = 10 kW
Ẇ = kW
3.Medium
TH​ = 500 °CTL​ = ?EQH​ = 3000 kJQL​ = 1060 kJW

A reversible (Carnot) heat engine takes in 3000 kJ of heat from a reservoir at 500 °C and rejects 1060 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 500 °CQH = 3000 kJQL = 1060 kJ
TL = °C
4.Medium
TH​ = 28 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 6 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 6 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 = 6 kW
Q̇H = kW
5.Hard
TH​ = 650 °CT0​ = 30 °CTL​ = -10 °CERWQ̇H​ = 10 kWQ̇L​ = ?

A Carnot heat engine receives 10 kW of heat from a source at 650 °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 -10 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 30 °CTL = -10 °CQ̇H = 10 kW
Q̇L = kW
6.Hard
TH​ = 20 °CTL​ = -5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -5 °C outside, delivering 11 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -5 °CQ̇H = 11 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 5.714 kW
  2. 2. Ẇ = 2.564 kW
  3. 3. TL = 0.02967 °C
  4. 4. Q̇H = 6.615 kW
  5. 5. Q̇L = 44.18 kW
  6. 6. Ẇmin = 0.9381 kW

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