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​ = 3400 kJQL​ = 2720 kJW = ?

A heat engine takes in 3400 kJ of heat from a hot reservoir and rejects 2720 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3400 kJQL = 2720 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4200 kJQL​ = 2730 kJW

A heat engine takes in 4200 kJ of heat from a hot reservoir and rejects 2730 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4200 kJQL = 2730 kJ
η = %
3.Medium
TH​ = 750 °CTL​ = 40 °CEQH​QL​η = 38%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 38%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 40 °Cη = 38%
ηII = %
4.Medium
TH​ = 525 °CTL​ = 35 °CEQH​ = 1800 kJQL​W = ?

A heat engine works between a hot reservoir at 525 °C and a cold reservoir at 35 °C. It takes in 1800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 525 °CTL = 35 °CQH = 1800 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 5 °CQ̇H = 7 kW
Ẇmin = kW
6.Hard
TH​ = 45 °CTL​ = 2 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump delivers 4 kW of heat to a heating system at 45 °C, taking heat from a source at 2 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = 2 °CηII = 60%Q̇H = 4 kW
Ẇ = kW

Answer key

  1. 1. W = 680 kJ
  2. 2. η = 35 %
  3. 3. ηII = 54.76 %
  4. 4. Wmax = 1105 kJ
  5. 5. Ẇmin = 0.4032 kW
  6. 6. Ẇ = 0.901 kW

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