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​ = 5.1 kWẆ = 1.7 kW

A refrigerator removes heat from its cold space at a rate of 5.1 kW while its compressor uses 1.7 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 5.1 kWẆ = 1.7 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 1500 kJQL​ = 825 kJW = ?

A heat engine takes in 1500 kJ of heat from a hot reservoir and rejects 825 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1500 kJQL = 825 kJ
W = kJ
3.Medium
TH​ = 775 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 775 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 775 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 525 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 525 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 525 °CTL = 30 °C
ηmax = %
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 5 °CQ̇H = 14 kW
Ẇmin = kW
6.Hard
TH​ = 450 °CT0​ = 20 °CTL​ = -15 °CERWQ̇H​ = 100 kWQ̇L​ = ?

A Carnot heat engine receives 100 kW of heat from a source at 450 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 450 °CT0 = 20 °CTL = -15 °CQ̇H = 100 kW
Q̇L = kW

Answer key

  1. 1. Q̇H = 6.8 kW
  2. 2. W = 675 kJ
  3. 3. ηmax = 71.08 %
  4. 4. ηmax = 62.02 %
  5. 5. Ẇmin = 0.8064 kW
  6. 6. Q̇L = 438.6 kW

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