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​ = 4200 kJQL​ = 2310 kJW

A heat engine takes in 4200 kJ of heat from a hot reservoir and rejects 2310 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4200 kJQL = 2310 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 35%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 100 MWη = 35%
Q̇L = MW
3.Medium
TH​ = 35 °CTL​ = -30 °CRQ̇H​ = ?Q̇L​ = 1.5 kWẆ

A reversible refrigerator keeps a cold room at -30 °C by removing 1.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -30 °CTH = 35 °CQ̇L = 1.5 kW
Q̇H = kW
4.Medium
TH​ = 325 °CTL​ = 5 °CEQH​ = 1800 kJQL​W = ?

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 5 °C. It takes in 1800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 325 °CTL = 5 °CQH = 1800 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 0 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 0 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 0 °CQ̇H = 8 kW
Ẇmin = kW
6.Hard
TH​ = 35 °CTL​ = -10 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -10 °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 = -10 °CQ̇L = 4 kW
Ẇmin = kW

Answer key

  1. 1. η = 45 %
  2. 2. Q̇L = 185.7 MW
  3. 3. Q̇H = 1.901 kW
  4. 4. Wmax = 963 kJ
  5. 5. Ẇmin = 0.5963 kW
  6. 6. Ẇmin = 0.684 kW

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