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
kitchencold spaceRQ̇H​Q̇L​ = 5.2 kWẆ = 2 kW

A refrigerator removes heat from its cold space at a rate of 5.2 kW while its compressor uses 2 kW of power. Find its coefficient of performance COPR.

Q̇L = 5.2 kWẆ = 2 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 500 MW

A power plant delivers a net power output of 500 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 500 MWη = 42%
Q̇L = MW
3.Medium
TH​ = 20 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 2 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 2 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -10 °CTH = 20 °CQ̇L = 2 kW
Q̇H = kW
4.Medium
TH​ = 35 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 9.5 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 9.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 35 °CQ̇L = 9.5 kW
Q̇H = kW
5.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -10 °CQ̇H = 7 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 14.5 kWQ̇L​Ẇ = ?

A heat pump delivers 14.5 kW of heat to a heating system at 21 °C, taking heat from a source at -10 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -10 °CηII = 35%Q̇H = 14.5 kW
Ẇ = kW

Answer key

  1. 1. COPR = 2.6
  2. 2. Q̇L = 690.5 MW
  3. 3. Q̇H = 2.228 kW
  4. 4. Q̇H = 11.47 kW
  5. 5. Ẇmin = 0.7164 kW
  6. 6. Ẇ = 4.366 kW

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