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
houseoutside airHPQ̇H​ = 8 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.2 delivers 8 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.2Q̇H = 8 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 3200 kJQL​ = 1920 kJW

A heat engine takes in 3200 kJ of heat from a hot reservoir and rejects 1920 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3200 kJQL = 1920 kJ
η = %
3.Medium
TH​ = 750 °CTL​ = 40 °CEQH​ = 1000 kJQL​W = ?

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 40 °C. It takes in 1000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 750 °CTL = 40 °CQH = 1000 kJ
Wmax = kJ
4.Medium
TH​ = 20 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 2 kWẆ

A reversible refrigerator keeps a cold room at -25 °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 = -25 °CTH = 20 °CQ̇L = 2 kW
Q̇H = kW
5.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 4 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -10 °CQ̇H = 4 kW
Ẇmin = kW
6.Hard
TH​ = 550 °CTL​ = 25 °CEQH​ = 3400 kJQL​ = 2108 kJW = 1292 kJ

A heat engine takes in 3400 kJ of heat from a reservoir at 550 °C, produces 1292 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 550 °CTL = 25 °CQH = 3400 kJW = 1292 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇L = 6.095 kW
  2. 2. η = 40 %
  3. 3. Wmax = 693.9 kJ
  4. 4. Q̇H = 2.363 kW
  5. 5. Ẇmin = 0.4337 kW
  6. 6. Sgen = 2.94 kJ/K

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