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​ = 3400 kJQL​ = 2720 kJW

A heat engine takes in 3400 kJ of heat from a hot reservoir and rejects 2720 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3400 kJQL = 2720 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 8.6 kWẆ = 2 kW

A refrigerator removes heat from its cold space at a rate of 8.6 kW while its compressor uses 2 kW of power. Find its coefficient of performance COPR.

Q̇L = 8.6 kWẆ = 2 kW
COPR =
3.Medium
TH​ = 625 °CTL​ = ?EQH​ = 4500 kJQL​ = 1469 kJW

A reversible (Carnot) heat engine takes in 4500 kJ of heat from a reservoir at 625 °C and rejects 1469 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 625 °CQH = 4500 kJQL = 1469 kJ
TL = °C
4.Medium
TH​ = 800 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 30 °C
ηmax = %
5.Hard
TH​ = 32 °CTL​ = -25 °CRQ̇H​Q̇L​ = 5 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 32 °C, removing heat from the cold space at 5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -25 °CQ̇L = 5 kW
Ẇmin = kW
6.Hard
TH​ = 600 °CT0​ = 20 °CTL​ = -20 °CERWQ̇H​ = 20 kWQ̇L​ = ?

A Carnot heat engine receives 20 kW of heat from a source at 600 °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 -20 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 600 °CT0 = 20 °CTL = -20 °CQ̇H = 20 kW
Q̇L = kW

Answer key

  1. 1. η = 20 %
  2. 2. COPR = 4.3
  3. 3. TL = 20.05 °C
  4. 4. ηmax = 71.75 %
  5. 5. Ẇmin = 1.148 kW
  6. 6. Q̇L = 84.08 kW

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