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​ = 4100 kJQL​ = 2255 kJW

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 2255 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4100 kJQL = 2255 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 3900 kJQL​ = 2535 kJW = ?

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2535 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3900 kJQL = 2535 kJ
W = kJ
3.Medium
TH​ = 750 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 750 °CTL = 10 °C
ηmax = %
4.Medium
TH​ = 500 °CTL​ = 30 °CEQH​QL​η = 30%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 30%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 30 °Cη = 30%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump delivers 15 kW of heat to a heating system at 21 °C, taking heat from a source at 7 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = 7 °CηII = 45%Q̇H = 15 kW
Ẇ = kW
6.Hard
TH​ = 55 °CTL​ = 7 °CHPQ̇H​ = 10.5 kWQ̇L​Ẇ = ?

A heat pump delivers 10.5 kW of heat to a heating system at 55 °C, taking heat from a source at 7 °C. Its actual COP is 40% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 7 °CηII = 40%Q̇H = 10.5 kW
Ẇ = kW

Answer key

  1. 1. η = 45 %
  2. 2. W = 1365 kJ
  3. 3. ηmax = 72.33 %
  4. 4. ηII = 49.35 %
  5. 5. Ẇ = 1.586 kW
  6. 6. Ẇ = 3.84 kW

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