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​ = 500 kJQL​ = 350 kJW = ?

A heat engine takes in 500 kJ of heat from a hot reservoir and rejects 350 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 500 kJQL = 350 kJ
W = kJ
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 7.8 kWẆ = 3 kW

A refrigerator removes heat from its cold space at a rate of 7.8 kW while its compressor uses 3 kW of power. Find its coefficient of performance COPR.

Q̇L = 7.8 kWẆ = 3 kW
COPR =
3.Medium
TH​ = 500 °CTL​ = 30 °CEQH​ = 2100 kJQL​W = ?

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 30 °C. It takes in 2100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 500 °CTL = 30 °CQH = 2100 kJ
Wmax = kJ
4.Medium
TH​ = 400 °CTL​ = 35 °CEQH​QL​η = 38%

A heat engine receives heat from a source at 400 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 38%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 400 °CTL = 35 °Cη = 38%
ηII = %
5.Hard
TH​ = 30 °CTL​ = 5 °CRQ̇H​Q̇L​ = 4.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 30 °C, removing heat from the cold space at 4.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 5 °CQ̇L = 4.5 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 7 °C outside, delivering 4 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 7 °CQ̇H = 4 kW
Ẇmin = kW

Answer key

  1. 1. W = 150 kJ
  2. 2. COPR = 2.6
  3. 3. Wmax = 1277 kJ
  4. 4. ηII = 70.08 %
  5. 5. Ẇmin = 0.4045 kW
  6. 6. Ẇmin = 0.1904 kW

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