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​ = 8.16 kWẆ = 2.4 kW

A refrigerator removes heat from its cold space at a rate of 8.16 kW while its compressor uses 2.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 8.16 kWẆ = 2.4 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 4000 kJQL​ = 2400 kJW = ?

A heat engine takes in 4000 kJ of heat from a hot reservoir and rejects 2400 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4000 kJQL = 2400 kJ
W = kJ
3.Medium
TH​ = 650 °CTL​ = 40 °CEQH​ = 500 kJQL​W = ?

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 40 °C. It takes in 500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 650 °CTL = 40 °CQH = 500 kJ
Wmax = kJ
4.Medium
TH​ = 350 °CTL​ = 20 °CEQH​ = 600 kJQL​W = ?

A heat engine works between a hot reservoir at 350 °C and a cold reservoir at 20 °C. It takes in 600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 350 °CTL = 20 °CQH = 600 kJ
Wmax = kJ
5.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

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

TH = 21 °CTL = 7 °CQ̇H = 7 kW
Ẇmin = kW
6.Hard
TH​ = 750 °CTL​ = 30 °CEQH​ = 700 kJQL​ = 455 kJW = 245 kJ

A heat engine takes in 700 kJ of heat from a reservoir at 750 °C, produces 245 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 30 °CQH = 700 kJW = 245 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇H = 10.56 kW
  2. 2. W = 1600 kJ
  3. 3. Wmax = 330.4 kJ
  4. 4. Wmax = 317.7 kJ
  5. 5. Ẇmin = 0.3332 kW
  6. 6. Sgen = 0.8167 kJ/K

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