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​ = 3500 kJQL​ = 2625 kJW = ?

A heat engine takes in 3500 kJ of heat from a hot reservoir and rejects 2625 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3500 kJQL = 2625 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 1500 kJQL​ = 825 kJW = ?

A heat engine takes in 1500 kJ of heat from a hot reservoir and rejects 825 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1500 kJQL = 825 kJ
W = kJ
3.Medium
TH​ = 850 °CTL​ = 40 °CEQH​QL​η = 40%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 40%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 40 °Cη = 40%
ηII = %
4.Medium
TH​ = 225 °CTL​ = 20 °CEQH​ = 1900 kJQL​W = ?

A heat engine works between a hot reservoir at 225 °C and a cold reservoir at 20 °C. It takes in 1900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 225 °CTL = 20 °CQH = 1900 kJ
Wmax = kJ
5.Hard
TH​ = 55 °CTL​ = 7 °CHPQ̇H​ = 9.5 kWQ̇L​Ẇ = ?

A heat pump delivers 9.5 kW of heat to a heating system at 55 °C, taking heat from a source at 7 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 7 °CηII = 50%Q̇H = 9.5 kW
Ẇ = kW
6.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 2 °CQ̇H = 7 kW
Ẇmin = kW

Answer key

  1. 1. W = 875 kJ
  2. 2. W = 675 kJ
  3. 3. ηII = 55.46 %
  4. 4. Wmax = 781.9 kJ
  5. 5. Ẇ = 2.779 kW
  6. 6. Ẇmin = 0.4522 kW

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