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​ = 16 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.7 delivers 16 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.7Q̇H = 16 kW
Q̇L = kW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 55%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 55%
Q̇L = MW
3.Medium
TH​ = 275 °CTL​ = 20 °CEQH​ = 1900 kJQL​W = ?

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 20 °C. It takes in 1900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 275 °CTL = 20 °CQH = 1900 kJ
Wmax = kJ
4.Medium
TH​ = 30 °CTL​ = 4 °CRQ̇H​ = ?Q̇L​ = 4.5 kWẆ

A reversible refrigerator keeps a cold room at 4 °C by removing 4.5 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = 4 °CTH = 30 °CQ̇L = 4.5 kW
Q̇H = kW
5.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 7 °CQ̇H = 5 kW
Ẇmin = kW
6.Hard
TH​ = 25 °CTL​ = -18 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 25 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = -18 °CQ̇L = 4 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 12.6 kW
  2. 2. Q̇L = 163.6 MW
  3. 3. Wmax = 883.9 kJ
  4. 4. Q̇H = 4.922 kW
  5. 5. Ẇmin = 0.2217 kW
  6. 6. Ẇmin = 0.6741 kW

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