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
hot reservoircold reservoirEQH​ = 1300 kJQL​ = 975 kJW

A heat engine takes in 1300 kJ of heat from a hot reservoir and rejects 975 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1300 kJQL = 975 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 30%
Q̇H = MW
3.Medium
TH​ = 40 °CTL​ = -5 °CRQ̇H​ = ?Q̇L​ = 2 kWẆ

A reversible refrigerator keeps a cold room at -5 °C by removing 2 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = -5 °CTH = 40 °CQ̇L = 2 kW
Q̇H = kW
4.Medium
TH​ = 700 °CTL​ = 15 °CEQH​ = 3600 kJQL​W = ?

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 15 °C. It takes in 3600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 700 °CTL = 15 °CQH = 3600 kJ
Wmax = kJ
5.Hard
TH​ = 28 °CTL​ = -10 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 28 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = -10 °CQ̇L = 3.5 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 6 kW
Ẇmin = kW

Answer key

  1. 1. η = 25 %
  2. 2. Q̇H = 666.7 MW
  3. 3. Q̇H = 2.336 kW
  4. 4. Wmax = 2534 kJ
  5. 5. Ẇmin = 0.5054 kW
  6. 6. Ẇmin = 0.4066 kW

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