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 = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 42%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 4100 kJQL​ = 2665 kJW = ?

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 2665 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4100 kJQL = 2665 kJ
W = kJ
3.Medium
TH​ = 400 °CTL​ = 25 °CEQH​QL​η = 36%

A heat engine receives heat from a source at 400 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 36%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 400 °CTL = 25 °Cη = 36%
ηII = %
4.Medium
TH​ = 800 °CTL​ = 20 °CEQH​QL​η = 44%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 44%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 20 °Cη = 44%
ηII = %
5.Hard
TH​ = 450 °CT0​ = 25 °CTL​ = 0 °CERWQ̇H​ = 150 kWQ̇L​ = ?

A Carnot heat engine receives 150 kW of heat from a source at 450 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at 0 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 450 °CT0 = 25 °CTL = 0 °CQ̇H = 150 kW
Q̇L = kW
6.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -10 °CQ̇H = 7 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 69.05 MW
  2. 2. W = 1435 kJ
  3. 3. ηII = 64.62 %
  4. 4. ηII = 60.54 %
  5. 5. Q̇L = 963.2 kW
  6. 6. Ẇmin = 0.7377 kW

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