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​ = 1200 kJQL​ = 960 kJW = ?

A heat engine takes in 1200 kJ of heat from a hot reservoir and rejects 960 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1200 kJQL = 960 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4600 kJQL​ = 2760 kJW = ?

A heat engine takes in 4600 kJ of heat from a hot reservoir and rejects 2760 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4600 kJQL = 2760 kJ
W = kJ
3.Medium
TH​ = 700 °CTL​ = 10 °CEQH​QL​η = 46%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 46%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 10 °Cη = 46%
ηII = %
4.Medium
TH​ = 600 °CTL​ = 15 °CEQH​ = 4100 kJQL​W = ?

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 15 °C. It takes in 4100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 600 °CTL = 15 °CQH = 4100 kJ
Wmax = kJ
5.Hard
TH​ = 35 °CTL​ = 5 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 35 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = 5 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 20 kWQ̇L​Ẇ = ?

A heat pump delivers 20 kW of heat to a heating system at 21 °C, taking heat from a source at -10 °C. Its actual COP is 40% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -10 °CηII = 40%Q̇H = 20 kW
Ẇ = kW

Answer key

  1. 1. W = 240 kJ
  2. 2. W = 1840 kJ
  3. 3. ηII = 64.88 %
  4. 4. Wmax = 2747 kJ
  5. 5. Ẇmin = 0.2157 kW
  6. 6. Ẇ = 5.269 kW

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