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
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 40%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 40%
Q̇L = MW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 2.04 kWẆ = 0.6 kW

A refrigerator removes heat from its cold space at a rate of 2.04 kW while its compressor uses 0.6 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 2.04 kWẆ = 0.6 kW
Q̇H = kW
3.Medium
TH​ = 450 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 450 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 275 °CTL​ = ?EQH​ = 3900 kJQL​ = 1979 kJW

A reversible (Carnot) heat engine takes in 3900 kJ of heat from a reservoir at 275 °C and rejects 1979 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 275 °CQH = 3900 kJQL = 1979 kJ
TL = °C
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump delivers 9 kW of heat to a heating system at 21 °C, taking heat from a source at -10 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -10 °CηII = 55%Q̇H = 9 kW
Ẇ = kW
6.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 7 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 5 °C outside, delivering 7 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 5 °CQ̇H = 7 kW
COPmax =

Answer key

  1. 1. Q̇L = 75 MW
  2. 2. Q̇H = 2.64 kW
  3. 3. ηmax = 57.39 %
  4. 4. TL = 5.001 °C
  5. 5. Ẇ = 1.725 kW
  6. 6. COPmax = 18.38

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