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​ = 1900 kJQL​ = 1140 kJW = ?

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1140 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1900 kJQL = 1140 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 3700 kJQL​ = 2035 kJW

A heat engine takes in 3700 kJ of heat from a hot reservoir and rejects 2035 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3700 kJQL = 2035 kJ
η = %
3.Medium
TH​ = 350 °CTL​ = 25 °CEQH​QL​η = 34%

A heat engine receives heat from a source at 350 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 34%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 350 °CTL = 25 °Cη = 34%
ηII = %
4.Medium
TH​ = 750 °CTL​ = 20 °CEQH​QL​η = 50%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 50%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 20 °Cη = 50%
ηII = %
5.Hard
TH​ = 750 °CTL​ = 10 °CEQH​ = 4400 kJQL​ = 1848 kJW = 2552 kJ

A heat engine takes in 4400 kJ of heat from a reservoir at 750 °C, produces 2552 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 10 °CQH = 4400 kJW = 2552 kJ
Sgen = kJ/K
6.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 4 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 4 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 2 °CQ̇H = 4 kW
COPmax =

Answer key

  1. 1. W = 760 kJ
  2. 2. η = 45 %
  3. 3. ηII = 65.19 %
  4. 4. ηII = 70.08 %
  5. 5. Sgen = 2.226 kJ/K
  6. 6. COPmax = 15.48

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