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 = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 35%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 100 MWη = 35%
Q̇H = MW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 400 MW

A power plant delivers a net power output of 400 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 400 MWη = 25%
Q̇L = MW
3.Medium
TH​ = 28 °CTL​ = 4 °CRQ̇H​ = ?Q̇L​ = 3.5 kWẆ

A reversible refrigerator keeps a cold room at 4 °C by removing 3.5 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = 4 °CTH = 28 °CQ̇L = 3.5 kW
Q̇H = kW
4.Medium
TH​ = 850 °CTL​ = 20 °CEQH​QL​η = 55%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 55%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 20 °Cη = 55%
ηII = %
5.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 17 kWQ̇L​Ẇ = ?

A heat pump delivers 17 kW of heat to a heating system at 20 °C, taking heat from a source at 0 °C. Its actual COP is 40% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = 0 °CηII = 40%Q̇H = 17 kW
Ẇ = kW
6.Hard
TH​ = 850 °CT0​ = 20 °CTL​ = -25 °CERWQ̇H​ = 110 kWQ̇L​ = ?

A Carnot heat engine receives 110 kW of heat from a source at 850 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -25 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 850 °CT0 = 20 °CTL = -25 °CQ̇H = 110 kW
Q̇L = kW

Answer key

  1. 1. Q̇H = 285.7 MW
  2. 2. Q̇L = 1200 MW
  3. 3. Q̇H = 3.803 kW
  4. 4. ηII = 74.43 %
  5. 5. Ẇ = 2.9 kW
  6. 6. Q̇L = 448.3 kW

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