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​ = 1700 kJQL​ = 1360 kJW

A heat engine takes in 1700 kJ of heat from a hot reservoir and rejects 1360 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1700 kJQL = 1360 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 11.7 kWẆ = 2.6 kW

A refrigerator removes heat from its cold space at a rate of 11.7 kW while its compressor uses 2.6 kW of power. Find its coefficient of performance COPR.

Q̇L = 11.7 kWẆ = 2.6 kW
COPR =
3.Medium
TH​ = 225 °CTL​ = 15 °CEQH​ = 2000 kJQL​W = ?

A heat engine works between a hot reservoir at 225 °C and a cold reservoir at 15 °C. It takes in 2000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 225 °CTL = 15 °CQH = 2000 kJ
Wmax = kJ
4.Medium
TH​ = 350 °CTL​ = ?EQH​ = 3500 kJQL​ = 1843 kJW

A reversible (Carnot) heat engine takes in 3500 kJ of heat from a reservoir at 350 °C and rejects 1843 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 350 °CQH = 3500 kJQL = 1843 kJ
TL = °C
5.Hard
TH​ = 25 °CTL​ = 2 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at 2 °C in a kitchen at 25 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 2 °CQ̇L = 3.5 kW
Ẇmin = kW
6.Hard
TH​ = 1000 °CT0​ = 30 °CTL​ = -5 °CERWQ̇H​ = 90 kWQ̇L​ = ?

A Carnot heat engine receives 90 kW of heat from a source at 1000 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -5 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 1000 °CT0 = 30 °CTL = -5 °CQ̇H = 90 kW
Q̇L = kW

Answer key

  1. 1. η = 20 %
  2. 2. COPR = 4.5
  3. 3. Wmax = 843.1 kJ
  4. 4. TL = 54.98 °C
  5. 5. Ẇmin = 0.2926 kW
  6. 6. Q̇L = 525.3 kW

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