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
hot reservoircold reservoirEQH​ = 1100 kJQL​ = 660 kJW

A heat engine takes in 1100 kJ of heat from a hot reservoir and rejects 660 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1100 kJQL = 660 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 3 kWẆ = 2 kW

A refrigerator removes heat from its cold space at a rate of 3 kW while its compressor uses 2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 3 kWẆ = 2 kW
Q̇H = kW
3.Medium
TH​ = 800 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 625 °CTL​ = 25 °CEQH​ = 4100 kJQL​W = ?

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 25 °C. It takes in 4100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 625 °CTL = 25 °CQH = 4100 kJ
Wmax = kJ
5.Hard
TH​ = 400 °CT0​ = 27 °CTL​ = -15 °CERWQ̇H​ = 160 kWQ̇L​ = ?

A Carnot heat engine receives 160 kW of heat from a source at 400 °C and rejects heat to the surroundings at 27 °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 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 400 °CT0 = 27 °CTL = -15 °CQ̇H = 160 kW
Q̇L = kW
6.Hard
TH​ = 850 °CTL​ = 35 °CEQH​ = 3000 kJQL​ = 1260 kJW = 1740 kJ

A heat engine takes in 3000 kJ of heat from a reservoir at 850 °C, produces 1740 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 850 °CTL = 35 °CQH = 3000 kJW = 1740 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 40 %
  2. 2. Q̇H = 5 kW
  3. 3. ηmax = 71.29 %
  4. 4. Wmax = 2739 kJ
  5. 5. Q̇L = 544.9 kW
  6. 6. Sgen = 1.418 kJ/K

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