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​ = 2.52 kWẆ = 1.2 kW

A refrigerator removes heat from its cold space at a rate of 2.52 kW while its compressor uses 1.2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.52 kWẆ = 1.2 kW
Q̇H = 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​ = 325 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 575 °CTL​ = 35 °CEQH​ = 800 kJQL​W = ?

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 35 °C. It takes in 800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 575 °CTL = 35 °CQH = 800 kJ
Wmax = kJ
5.Hard
TH​ = 35 °CTL​ = 10 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump delivers 10 kW of heat to a heating system at 35 °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 = 35 °CTL = 10 °CηII = 30%Q̇H = 10 kW
Ẇ = kW
6.Hard
TH​ = 28 °CTL​ = 5 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 28 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = 5 °CQ̇L = 3.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 3.72 kW
  2. 2. COPR = 2.6
  3. 3. ηmax = 47.65 %
  4. 4. Wmax = 509.3 kJ
  5. 5. Ẇ = 2.704 kW
  6. 6. Ẇmin = 0.2894 kW

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