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
kitchencold spaceRQ̇H​Q̇L​ = 1.02 kWẆ = 0.6 kW

A refrigerator removes heat from its cold space at a rate of 1.02 kW while its compressor uses 0.6 kW of power. Find its coefficient of performance COPR.

Q̇L = 1.02 kWẆ = 0.6 kW
COPR =
2.Easy
hot reservoircold reservoirEQH​ = 1900 kJQL​ = 1140 kJW

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1140 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1900 kJQL = 1140 kJ
η = %
3.Medium
TH​ = 300 °CTL​ = 25 °CEQH​ = 4500 kJQL​W = ?

A heat engine works between a hot reservoir at 300 °C and a cold reservoir at 25 °C. It takes in 4500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 300 °CTL = 25 °CQH = 4500 kJ
Wmax = kJ
4.Medium
TH​ = 200 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 200 °CTL = 10 °C
ηmax = %
5.Hard
TH​ = 28 °CTL​ = 4 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 28 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = 4 °CQ̇L = 3.5 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 5 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 5 °CQ̇H = 14 kW
Ẇmin = kW

Answer key

  1. 1. COPR = 1.7
  2. 2. η = 40 %
  3. 3. Wmax = 2159 kJ
  4. 4. ηmax = 40.16 %
  5. 5. Ẇmin = 0.3031 kW
  6. 6. Ẇmin = 0.7615 kW

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