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 = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 35%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 300 MWη = 35%
Q̇H = MW
2.Easy
houseoutside airHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.9 delivers 4 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.9Q̇H = 4 kW
Ẇ = kW
3.Medium
TH​ = 35 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 0.5 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 0.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 35 °CQ̇L = 0.5 kW
Q̇H = kW
4.Medium
TH​ = 375 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 375 °CTL = 20 °C
ηmax = %
5.Hard
TH​ = 30 °CTL​ = 2 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at 2 °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 = 2 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 20 °CTL​ = -5 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -5 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -5 °CQ̇H = 13 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 857.1 MW
  2. 2. Ẇ = 1.026 kW
  3. 3. Q̇H = 0.6086 kW
  4. 4. ηmax = 54.77 %
  5. 5. Ẇmin = 0.2035 kW
  6. 6. Ẇmin = 1.109 kW

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