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​ = 2.4 kWẆ = 1.2 kW

A refrigerator removes heat from its cold space at a rate of 2.4 kW while its compressor uses 1.2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.4 kWẆ = 1.2 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 4700 kJQL​ = 2820 kJW

A heat engine takes in 4700 kJ of heat from a hot reservoir and rejects 2820 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4700 kJQL = 2820 kJ
η = %
3.Medium
TH​ = 600 °CTL​ = ?EQH​ = 1100 kJQL​ = 350 kJW

A reversible (Carnot) heat engine takes in 1100 kJ of heat from a reservoir at 600 °C and rejects 350 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 600 °CQH = 1100 kJQL = 350 kJ
TL = °C
4.Medium
TH​ = 350 °CTL​ = 15 °CEQH​ = 4800 kJQL​W = ?

A heat engine works between a hot reservoir at 350 °C and a cold reservoir at 15 °C. It takes in 4800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 350 °CTL = 15 °CQH = 4800 kJ
Wmax = kJ
5.Hard
TH​ = 550 °CTL​ = 40 °CEQH​ = 1000 kJQL​ = 500 kJW = 500 kJ

A heat engine takes in 1000 kJ of heat from a reservoir at 550 °C, produces 500 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 550 °CTL = 40 °CQH = 1000 kJW = 500 kJ
Sgen = kJ/K
6.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 7 °CQ̇H = 14 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 3.6 kW
  2. 2. η = 40 %
  3. 3. TL = 4.67 °C
  4. 4. Wmax = 2580 kJ
  5. 5. Sgen = 0.3818 kJ/K
  6. 6. Ẇmin = 0.6208 kW

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