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​ = 3.33 kWẆ = 0.9 kW

A refrigerator removes heat from its cold space at a rate of 3.33 kW while its compressor uses 0.9 kW of power. Find its coefficient of performance COPR.

Q̇L = 3.33 kWẆ = 0.9 kW
COPR =
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 1.04 kWẆ = 0.4 kW

A refrigerator removes heat from its cold space at a rate of 1.04 kW while its compressor uses 0.4 kW of power. Find its coefficient of performance COPR.

Q̇L = 1.04 kWẆ = 0.4 kW
COPR =
3.Medium
TH​ = 20 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 4 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 4 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 = 4 kW
Q̇H = kW
4.Medium
TH​ = 550 °CTL​ = 10 °CEQH​ = 4500 kJQL​W = ?

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 10 °C. It takes in 4500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 550 °CTL = 10 °CQH = 4500 kJ
Wmax = kJ
5.Hard
TH​ = 30 °CTL​ = -10 °CRQ̇H​Q̇L​ = 0.5 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 30 °C, removing heat from the cold space at 0.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -10 °CQ̇L = 0.5 kW
Ẇmin = kW
6.Hard
TH​ = 35 °CTL​ = -5 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump delivers 5 kW of heat to a heating system at 35 °C, taking heat from a source at -5 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 35 °CTL = -5 °CηII = 50%Q̇H = 5 kW
Ẇ = kW

Answer key

  1. 1. COPR = 3.7
  2. 2. COPR = 2.6
  3. 3. Q̇H = 4.456 kW
  4. 4. Wmax = 2952 kJ
  5. 5. Ẇmin = 0.076 kW
  6. 6. Ẇ = 1.298 kW

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