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 = 500 MW

A power plant delivers a net power output of 500 MW with a thermal efficiency of 35%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 500 MWη = 35%
Q̇H = MW
2.Easy
houseoutside airHPQ̇H​ = 16.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.2 delivers 16.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.2Q̇H = 16.5 kW
Ẇ = kW
3.Medium
TH​ = 600 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 600 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 600 °CTL​ = 20 °CEQH​QL​η = 50%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 50%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 20 °Cη = 50%
ηII = %
5.Hard
TH​ = 28 °CTL​ = 4 °CRQ̇H​Q̇L​ = 2.5 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 28 °C, removing heat from the cold space at 2.5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = 4 °CQ̇L = 2.5 kW
Ẇmin = kW
6.Hard
TH​ = 55 °CTL​ = -5 °CHPQ̇H​ = 12.5 kWQ̇L​Ẇ = ?

A heat pump delivers 12.5 kW of heat to a heating system at 55 °C, taking heat from a source at -5 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = -5 °CηII = 35%Q̇H = 12.5 kW
Ẇ = kW

Answer key

  1. 1. Q̇H = 1429 MW
  2. 2. Ẇ = 5.156 kW
  3. 3. ηmax = 66.43 %
  4. 4. ηII = 75.27 %
  5. 5. Ẇmin = 0.2165 kW
  6. 6. Ẇ = 6.53 kW

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