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​ = 2900 kJQL​ = 2320 kJW = ?

A heat engine takes in 2900 kJ of heat from a hot reservoir and rejects 2320 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2900 kJQL = 2320 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 5000 kJQL​ = 4000 kJW

A heat engine takes in 5000 kJ of heat from a hot reservoir and rejects 4000 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 5000 kJQL = 4000 kJ
η = %
3.Medium
TH​ = 575 °CTL​ = 15 °CEQH​ = 3200 kJQL​W = ?

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 15 °C. It takes in 3200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 575 °CTL = 15 °CQH = 3200 kJ
Wmax = kJ
4.Medium
TH​ = 450 °CTL​ = 30 °CEQH​QL​η = 32%

A heat engine receives heat from a source at 450 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 32%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 450 °CTL = 30 °Cη = 32%
ηII = %
5.Hard
TH​ = 28 °CTL​ = 4 °CRQ̇H​Q̇L​ = 4.5 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 28 °C, removing heat from the cold space at 4.5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = 4 °CQ̇L = 4.5 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump delivers 14 kW of heat to a heating system at 21 °C, taking heat from a source at -5 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -5 °CηII = 50%Q̇H = 14 kW
Ẇ = kW

Answer key

  1. 1. W = 580 kJ
  2. 2. η = 20 %
  3. 3. Wmax = 2113 kJ
  4. 4. ηII = 55.1 %
  5. 5. Ẇmin = 0.3897 kW
  6. 6. Ẇ = 2.475 kW

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