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 30%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 600 MWη = 30%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 1600 kJQL​ = 960 kJW = ?

A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 960 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1600 kJQL = 960 kJ
W = kJ
3.Medium
TH​ = 400 °CTL​ = 20 °CEQH​QL​η = 31%

A heat engine receives heat from a source at 400 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 31%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 400 °CTL = 20 °Cη = 31%
ηII = %
4.Medium
TH​ = 850 °CTL​ = 35 °CEQH​QL​η = 54%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 54%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 35 °Cη = 54%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 2 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 0 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 0 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 0 °CQ̇H = 10 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 1400 MW
  2. 2. W = 640 kJ
  3. 3. ηII = 54.91 %
  4. 4. ηII = 74.42 %
  5. 5. Ẇmin = 0.6459 kW
  6. 6. Ẇmin = 0.7454 kW

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