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​ = 0.87 kWẆ = 0.3 kW

A refrigerator removes heat from its cold space at a rate of 0.87 kW while its compressor uses 0.3 kW of power. Find its coefficient of performance COPR.

Q̇L = 0.87 kWẆ = 0.3 kW
COPR =
2.Easy
hot reservoircold reservoirEQH​ = 1400 kJQL​ = 1050 kJW

A heat engine takes in 1400 kJ of heat from a hot reservoir and rejects 1050 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1400 kJQL = 1050 kJ
η = %
3.Medium
TH​ = 375 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 375 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 250 °CTL​ = ?EQH​ = 2300 kJQL​ = 1355 kJW

A reversible (Carnot) heat engine takes in 2300 kJ of heat from a reservoir at 250 °C and rejects 1355 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 250 °CQH = 2300 kJQL = 1355 kJ
TL = °C
5.Hard
TH​ = 1000 °CT0​ = 30 °CTL​ = -5 °CERWQ̇H​ = 10 kWQ̇L​ = ?

A Carnot heat engine receives 10 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 = 10 kW
Q̇L = kW
6.Hard
TH​ = 32 °CTL​ = -25 °CRQ̇H​Q̇L​ = 4.5 kWẆ

A refrigerator keeps its cold space at -25 °C in a kitchen at 32 °C, removing heat from the cold space at 4.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = -25 °CQ̇L = 4.5 kW
COPmax =

Answer key

  1. 1. COPR = 2.9
  2. 2. η = 25 %
  3. 3. ηmax = 51.69 %
  4. 4. TL = 35.05 °C
  5. 5. Q̇L = 58.37 kW
  6. 6. COPmax = 4.354

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