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​ = 1900 kJQL​ = 1330 kJW

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1330 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1900 kJQL = 1330 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 2.05 kWẆ = 0.5 kW

A refrigerator removes heat from its cold space at a rate of 2.05 kW while its compressor uses 0.5 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.05 kWẆ = 0.5 kW
Q̇H = kW
3.Medium
TH​ = 475 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 475 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 475 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 450 °CTL​ = 30 °CEQH​ = 3600 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 30 °C. It takes in 3600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 30 °CQH = 3600 kJ
Wmax = kJ
5.Hard
TH​ = 900 °CT0​ = 25 °CTL​ = 0 °CERWQ̇H​ = 60 kWQ̇L​ = ?

A Carnot heat engine receives 60 kW of heat from a source at 900 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at 0 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 900 °CT0 = 25 °CTL = 0 °CQ̇H = 60 kW
Q̇L = kW
6.Hard
TH​ = 750 °CTL​ = 35 °CEQH​ = 5000 kJQL​ = 3250 kJW = 1750 kJ

A heat engine takes in 5000 kJ of heat from a reservoir at 750 °C, produces 1750 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 35 °CQH = 5000 kJW = 1750 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 30 %
  2. 2. Q̇H = 2.55 kW
  3. 3. ηmax = 61.48 %
  4. 4. Wmax = 2091 kJ
  5. 5. Q̇L = 489 kW
  6. 6. Sgen = 5.66 kJ/K

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