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​ = 2200 kJQL​ = 1320 kJW = ?

A heat engine takes in 2200 kJ of heat from a hot reservoir and rejects 1320 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2200 kJQL = 1320 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 1600 kJQL​ = 1280 kJW

A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 1280 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1600 kJQL = 1280 kJ
η = %
3.Medium
TH​ = 550 °CTL​ = 10 °CEQH​QL​η = 39%

A heat engine receives heat from a source at 550 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 39%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 550 °CTL = 10 °Cη = 39%
ηII = %
4.Medium
TH​ = 750 °CTL​ = 15 °CEQH​ = 4300 kJQL​W = ?

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 15 °C. It takes in 4300 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 750 °CTL = 15 °CQH = 4300 kJ
Wmax = kJ
5.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 7 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 7 °CQ̇H = 15 kW
Ẇmin = kW
6.Hard
TH​ = 45 °CTL​ = -5 °CHPQ̇H​ = 12.5 kWQ̇L​Ẇ = ?

A heat pump delivers 12.5 kW of heat to a heating system at 45 °C, taking heat from a source at -5 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = -5 °CηII = 60%Q̇H = 12.5 kW
Ẇ = kW

Answer key

  1. 1. W = 880 kJ
  2. 2. η = 20 %
  3. 3. ηII = 59.45 %
  4. 4. Wmax = 3089 kJ
  5. 5. Ẇmin = 0.7139 kW
  6. 6. Ẇ = 3.274 kW

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