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​ = 3.36 kWẆ = 2.1 kW

A refrigerator removes heat from its cold space at a rate of 3.36 kW while its compressor uses 2.1 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 3.36 kWẆ = 2.1 kW
Q̇H = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 30%
Q̇H = MW
3.Medium
TH​ = 550 °CTL​ = 20 °CEQH​QL​η = 35%

A heat engine receives heat from a source at 550 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 35%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 550 °CTL = 20 °Cη = 35%
ηII = %
4.Medium
TH​ = 700 °CTL​ = ?EQH​ = 2000 kJQL​ = 613 kJW

A reversible (Carnot) heat engine takes in 2000 kJ of heat from a reservoir at 700 °C and rejects 613 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 700 °CQH = 2000 kJQL = 613 kJ
TL = °C
5.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 11 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 11 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = -10 °CQ̇H = 11 kW
COPmax =
6.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -10 °CQ̇H = 14 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 5.46 kW
  2. 2. Q̇H = 2000 MW
  3. 3. ηII = 54.36 %
  4. 4. TL = 25.12 °C
  5. 5. COPmax = 9.772
  6. 6. Ẇmin = 1.433 kW

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