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 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 500 MWη = 25%
Q̇L = MW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 4.25 kWẆ = 2.5 kW

A refrigerator removes heat from its cold space at a rate of 4.25 kW while its compressor uses 2.5 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 4.25 kWẆ = 2.5 kW
Q̇H = kW
3.Medium
TH​ = 775 °CTL​ = 25 °CEQH​ = 2900 kJQL​W = ?

A heat engine works between a hot reservoir at 775 °C and a cold reservoir at 25 °C. It takes in 2900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 775 °CTL = 25 °CQH = 2900 kJ
Wmax = kJ
4.Medium
TH​ = 35 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 6.5 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 6.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 35 °CQ̇L = 6.5 kW
Q̇H = kW
5.Hard
TH​ = 35 °CTL​ = 4 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at 4 °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 = 4 °CQ̇L = 4 kW
Ẇmin = kW
6.Hard
TH​ = 30 °CTL​ = -10 °CRQ̇H​Q̇L​ = 3 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 30 °C, removing heat from the cold space at 3 kW. Find the highest possible coefficient of performance COPmax.

TH = 30 °CTL = -10 °CQ̇L = 3 kW
COPmax =

Answer key

  1. 1. Q̇L = 1500 MW
  2. 2. Q̇H = 6.75 kW
  3. 3. Wmax = 2075 kJ
  4. 4. Q̇H = 7.85 kW
  5. 5. Ẇmin = 0.4474 kW
  6. 6. COPmax = 6.579

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