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 = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 35%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 35%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 4500 kJQL​ = 3375 kJW

A heat engine takes in 4500 kJ of heat from a hot reservoir and rejects 3375 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4500 kJQL = 3375 kJ
η = %
3.Medium
TH​ = 275 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 275 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 900 °CTL​ = 40 °CEQH​QL​η = 37%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 37%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 40 °Cη = 37%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 650 °CT0​ = 20 °CTL​ = -30 °CERWQ̇H​ = 10 kWQ̇L​ = ?

A Carnot heat engine receives 10 kW of heat from a source at 650 °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 -30 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 20 °CTL = -30 °CQ̇H = 10 kW
Q̇L = kW

Answer key

  1. 1. Q̇L = 371.4 MW
  2. 2. η = 25 %
  3. 3. ηmax = 46.52 %
  4. 4. ηII = 50.47 %
  5. 5. Ẇmin = 0.6776 kW
  6. 6. Q̇L = 33.19 kW

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