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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 33%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 33%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 3700 kJQL​ = 2405 kJW

A heat engine takes in 3700 kJ of heat from a hot reservoir and rejects 2405 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3700 kJQL = 2405 kJ
η = %
3.Medium
TH​ = 600 °CTL​ = 40 °CEQH​QL​η = 38%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 38%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 40 °Cη = 38%
ηII = %
4.Medium
TH​ = 500 °CTL​ = 25 °CEQH​QL​η = 31%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 31%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 25 °Cη = 31%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump delivers 6 kW of heat to a heating system at 21 °C, taking heat from a source at 7 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = 7 °CηII = 35%Q̇H = 6 kW
Ẇ = kW
6.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 4 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 0 °CQ̇H = 4 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 1818 MW
  2. 2. η = 35 %
  3. 3. ηII = 59.25 %
  4. 4. ηII = 50.46 %
  5. 5. Ẇ = 0.8159 kW
  6. 6. Ẇmin = 0.2729 kW

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