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
hot reservoircold reservoirEQH​ = 4800 kJQL​ = 3360 kJW = ?

A heat engine takes in 4800 kJ of heat from a hot reservoir and rejects 3360 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4800 kJQL = 3360 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 300 MWη = 25%
Q̇L = MW
3.Medium
TH​ = 275 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 275 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 650 °CTL​ = 35 °CEQH​QL​η = 37%

A heat engine receives heat from a source at 650 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 37%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 650 °CTL = 35 °Cη = 37%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 12 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 12 kW
Ẇmin = kW
6.Hard
TH​ = 1000 °CT0​ = 27 °CTL​ = -5 °CERWQ̇H​ = 160 kWQ̇L​ = ?

A Carnot heat engine receives 160 kW of heat from a source at 1000 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -5 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 1000 °CT0 = 27 °CTL = -5 °CQ̇H = 160 kW
Q̇L = kW

Answer key

  1. 1. W = 1440 kJ
  2. 2. Q̇L = 900 MW
  3. 3. ηmax = 49.26 %
  4. 4. ηII = 55.54 %
  5. 5. Ẇmin = 0.8131 kW
  6. 6. Q̇L = 1025 kW

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