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​ = 8.8 kWẆ = 2.2 kW

A refrigerator removes heat from its cold space at a rate of 8.8 kW while its compressor uses 2.2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 8.8 kWẆ = 2.2 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 3700 kJQL​ = 2220 kJW = ?

A heat engine takes in 3700 kJ of heat from a hot reservoir and rejects 2220 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3700 kJQL = 2220 kJ
W = kJ
3.Medium
TH​ = 20 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 2 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 2 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 20 °CQ̇L = 2 kW
Q̇H = kW
4.Medium
TH​ = 600 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 600 °CTL = 40 °C
ηmax = %
5.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -10 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 9 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 9 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 5 °CQ̇H = 9 kW
COPmax =

Answer key

  1. 1. Q̇H = 11 kW
  2. 2. W = 1480 kJ
  3. 3. Q̇H = 2.316 kW
  4. 4. ηmax = 64.14 %
  5. 5. Ẇmin = 1.023 kW
  6. 6. COPmax = 17.36

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