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​ = 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 =
2.Easy
hot reservoircold reservoirEQH​ = 2500 kJQL​ = 1875 kJW

A heat engine takes in 2500 kJ of heat from a hot reservoir and rejects 1875 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2500 kJQL = 1875 kJ
η = %
3.Medium
TH​ = 250 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 10 °C
ηmax = %
4.Medium
TH​ = 275 °CTL​ = ?EQH​ = 800 kJQL​ = 464 kJW

A reversible (Carnot) heat engine takes in 800 kJ of heat from a reservoir at 275 °C and rejects 464 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 275 °CQH = 800 kJQL = 464 kJ
TL = °C
5.Hard
TH​ = 950 °CT0​ = 27 °CTL​ = 0 °CERWQ̇H​ = 30 kWQ̇L​ = ?

A Carnot heat engine receives 30 kW of heat from a source at 950 °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 0 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 950 °CT0 = 27 °CTL = 0 °CQ̇H = 30 kW
Q̇L = kW
6.Hard
TH​ = 650 °CT0​ = 25 °CTL​ = -20 °CERWQ̇H​ = 90 kWQ̇L​ = ?

A Carnot heat engine receives 90 kW of heat from a source at 650 °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 -20 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 25 °CTL = -20 °CQ̇H = 90 kW
Q̇L = kW

Answer key

  1. 1. COPR = 4.5
  2. 2. η = 25 %
  3. 3. ηmax = 45.88 %
  4. 4. TL = 44.78 °C
  5. 5. Q̇L = 229 kW
  6. 6. Q̇L = 342.8 kW

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