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​ = 4200 kJQL​ = 2310 kJW

A heat engine takes in 4200 kJ of heat from a hot reservoir and rejects 2310 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4200 kJQL = 2310 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 2.24 kWẆ = 0.7 kW

A refrigerator removes heat from its cold space at a rate of 2.24 kW while its compressor uses 0.7 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.24 kWẆ = 0.7 kW
COPR =
3.Medium
TH​ = 850 °CTL​ = 40 °CEQH​QL​η = 54%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 54%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 40 °Cη = 54%
ηII = %
4.Medium
TH​ = 225 °CTL​ = ?EQH​ = 4200 kJQL​ = 2472 kJW

A reversible (Carnot) heat engine takes in 4200 kJ of heat from a reservoir at 225 °C and rejects 2472 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 225 °CQH = 4200 kJQL = 2472 kJ
TL = °C
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 16.5 kWQ̇L​Ẇ = ?

A heat pump delivers 16.5 kW of heat to a heating system at 22 °C, taking heat from a source at 5 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 5 °CηII = 35%Q̇H = 16.5 kW
Ẇ = kW
6.Hard
TH​ = 550 °CT0​ = 20 °CTL​ = -5 °CERWQ̇H​ = 110 kWQ̇L​ = ?

A Carnot heat engine receives 110 kW of heat from a source at 550 °C and rejects heat to the surroundings at 20 °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 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 550 °CT0 = 20 °CTL = -5 °CQ̇H = 110 kW
Q̇L = kW

Answer key

  1. 1. η = 45 %
  2. 2. COPR = 3.2
  3. 3. ηII = 74.88 %
  4. 4. TL = 20.05 °C
  5. 5. Ẇ = 2.715 kW
  6. 6. Q̇L = 759.7 kW

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