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​ = 1600 kJQL​ = 1120 kJW = ?

A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 1120 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1600 kJQL = 1120 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 2400 kJQL​ = 1800 kJW

A heat engine takes in 2400 kJ of heat from a hot reservoir and rejects 1800 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2400 kJQL = 1800 kJ
η = %
3.Medium
TH​ = 700 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 700 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 450 °CTL​ = 35 °CEQH​QL​η = 43%

A heat engine receives heat from a source at 450 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 43%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 450 °CTL = 35 °Cη = 43%
ηII = %
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -10 °CQ̇H = 5 kW
Ẇmin = kW
6.Hard
TH​ = 350 °CTL​ = 10 °CEQH​ = 1100 kJQL​ = 616 kJW = 484 kJ

A heat engine takes in 1100 kJ of heat from a reservoir at 350 °C, produces 484 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 350 °CTL = 10 °CQH = 1100 kJW = 484 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 480 kJ
  2. 2. η = 25 %
  3. 3. ηmax = 71.42 %
  4. 4. ηII = 74.93 %
  5. 5. Ẇmin = 0.5269 kW
  6. 6. Sgen = 0.4103 kJ/K

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