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​ = 1100 kJQL​ = 660 kJW = ?

A heat engine takes in 1100 kJ of heat from a hot reservoir and rejects 660 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1100 kJQL = 660 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 3000 kJQL​ = 1650 kJW = ?

A heat engine takes in 3000 kJ of heat from a hot reservoir and rejects 1650 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3000 kJQL = 1650 kJ
W = kJ
3.Medium
TH​ = 350 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 350 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 350 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 800 °CTL​ = 20 °CEQH​QL​η = 55%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 55%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 20 °Cη = 55%
ηII = %
5.Hard
TH​ = 30 °CTL​ = 4 °CRQ̇H​Q̇L​ = 3 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 30 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 4 °CQ̇L = 3 kW
Ẇmin = kW
6.Hard
TH​ = 350 °CTL​ = 40 °CEQH​ = 1600 kJQL​ = 960 kJW = 640 kJ

A heat engine takes in 1600 kJ of heat from a reservoir at 350 °C, produces 640 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 350 °CTL = 40 °CQH = 1600 kJW = 640 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 440 kJ
  2. 2. W = 1350 kJ
  3. 3. ηmax = 49.75 %
  4. 4. ηII = 75.67 %
  5. 5. Ẇmin = 0.2814 kW
  6. 6. Sgen = 0.498 kJ/K

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