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 = 1000 MW

A power plant delivers a net power output of 1000 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 1000 MWη = 30%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 3300 kJQL​ = 1815 kJW

A heat engine takes in 3300 kJ of heat from a hot reservoir and rejects 1815 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3300 kJQL = 1815 kJ
η = %
3.Medium
TH​ = 28 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 2 kWẆ

A reversible refrigerator keeps a cold room at -25 °C by removing 2 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -25 °CTH = 28 °CQ̇L = 2 kW
Q̇H = kW
4.Medium
TH​ = 25 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 5 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 5 kW of heat, and rejects heat to the surroundings at 25 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 25 °CQ̇L = 5 kW
Q̇H = kW
5.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -5 °CQ̇H = 5 kW
Ẇmin = kW
6.Hard
TH​ = 25 °CTL​ = 5 °CRQ̇H​Q̇L​ = 4.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 25 °C, removing heat from the cold space at 4.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 5 °CQ̇L = 4.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 3333 MW
  2. 2. η = 45 %
  3. 3. Q̇H = 2.427 kW
  4. 4. Q̇H = 5.889 kW
  5. 5. Ẇmin = 0.442 kW
  6. 6. Ẇmin = 0.3236 kW

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