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​ = 8.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.1 delivers 8.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.1Q̇H = 8.5 kW
Q̇L = kW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 3.12 kWẆ = 1.2 kW

A refrigerator removes heat from its cold space at a rate of 3.12 kW while its compressor uses 1.2 kW of power. Find its coefficient of performance COPR.

Q̇L = 3.12 kWẆ = 1.2 kW
COPR =
3.Medium
TH​ = 300 °CTL​ = 35 °CEQH​QL​η = 25%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 25%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 35 °Cη = 25%
ηII = %
4.Medium
TH​ = 675 °CTL​ = 5 °CEQH​ = 4000 kJQL​W = ?

A heat engine works between a hot reservoir at 675 °C and a cold reservoir at 5 °C. It takes in 4000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 675 °CTL = 5 °CQH = 4000 kJ
Wmax = kJ
5.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 10.5 kWQ̇L​Ẇ = ?

A heat pump delivers 10.5 kW of heat to a heating system at 20 °C, taking heat from a source at 7 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = 7 °CηII = 55%Q̇H = 10.5 kW
Ẇ = kW
6.Hard
TH​ = 45 °CTL​ = -10 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump delivers 5 kW of heat to a heating system at 45 °C, taking heat from a source at -10 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = -10 °CηII = 30%Q̇H = 5 kW
Ẇ = kW

Answer key

  1. 1. Q̇L = 6.427 kW
  2. 2. COPR = 2.6
  3. 3. ηII = 54.07 %
  4. 4. Wmax = 2827 kJ
  5. 5. Ẇ = 0.8466 kW
  6. 6. Ẇ = 2.881 kW

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