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​ = 4.08 kWẆ = 2.4 kW

A refrigerator removes heat from its cold space at a rate of 4.08 kW while its compressor uses 2.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 4.08 kWẆ = 2.4 kW
Q̇H = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 500 MW

A power plant delivers a net power output of 500 MW with a thermal efficiency of 38%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 500 MWη = 38%
Q̇H = MW
3.Medium
TH​ = 650 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 650 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 550 °CTL​ = 35 °CEQH​ = 3800 kJQL​W = ?

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 35 °C. It takes in 3800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 550 °CTL = 35 °CQH = 3800 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 18.5 kWQ̇L​Ẇ = ?

A heat pump delivers 18.5 kW of heat to a heating system at 22 °C, taking heat from a source at 5 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 5 °CηII = 45%Q̇H = 18.5 kW
Ẇ = kW
6.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 10 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 10 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 5 °CQ̇H = 10 kW
COPmax =

Answer key

  1. 1. Q̇H = 6.48 kW
  2. 2. Q̇H = 1316 MW
  3. 3. ηmax = 66.62 %
  4. 4. Wmax = 2377 kJ
  5. 5. Ẇ = 2.368 kW
  6. 6. COPmax = 17.36

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