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​ = 2100 kJQL​ = 1575 kJW = ?

A heat engine takes in 2100 kJ of heat from a hot reservoir and rejects 1575 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2100 kJQL = 1575 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4900 kJQL​ = 2940 kJW

A heat engine takes in 4900 kJ of heat from a hot reservoir and rejects 2940 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4900 kJQL = 2940 kJ
η = %
3.Medium
TH​ = 450 °CTL​ = 20 °CEQH​QL​η = 30%

A heat engine receives heat from a source at 450 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 30%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 450 °CTL = 20 °Cη = 30%
ηII = %
4.Medium
TH​ = 750 °CTL​ = 25 °CEQH​QL​η = 46%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 46%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 25 °Cη = 46%
ηII = %
5.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 9 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 0 °CQ̇H = 9 kW
Ẇmin = kW
6.Hard
TH​ = 32 °CTL​ = 4 °CRQ̇H​Q̇L​ = 0.5 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 32 °C, removing heat from the cold space at 0.5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = 4 °CQ̇L = 0.5 kW
Ẇmin = kW

Answer key

  1. 1. W = 525 kJ
  2. 2. η = 40 %
  3. 3. ηII = 50.45 %
  4. 4. ηII = 64.92 %
  5. 5. Ẇmin = 0.614 kW
  6. 6. Ẇmin = 0.05051 kW

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