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​ = 2.1 kWẆ = 0.5 kW

A refrigerator removes heat from its cold space at a rate of 2.1 kW while its compressor uses 0.5 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.1 kWẆ = 0.5 kW
Q̇H = kW
2.Easy
houseoutside airHPQ̇H​ = 15 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.5 delivers 15 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.5Q̇H = 15 kW
Q̇L = kW
3.Medium
TH​ = 300 °CTL​ = 15 °CEQH​QL​η = 25%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 25%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 15 °Cη = 25%
ηII = %
4.Medium
TH​ = 750 °CTL​ = ?EQH​ = 600 kJQL​ = 169 kJW

A reversible (Carnot) heat engine takes in 600 kJ of heat from a reservoir at 750 °C and rejects 169 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 750 °CQH = 600 kJQL = 169 kJ
TL = °C
5.Hard
TH​ = 30 °CTL​ = -10 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 30 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -10 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 35 °CTL​ = -25 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 35 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = -25 °CQ̇L = 4 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 2.6 kW
  2. 2. Q̇L = 11.67 kW
  3. 3. ηII = 50.28 %
  4. 4. TL = 15.04 °C
  5. 5. Ẇmin = 0.304 kW
  6. 6. Ẇmin = 0.9672 kW

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