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 = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 30%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 30%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 2100 kJQL​ = 1260 kJW

A heat engine takes in 2100 kJ of heat from a hot reservoir and rejects 1260 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2100 kJQL = 1260 kJ
η = %
3.Medium
TH​ = 575 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 575 °CTL = 25 °C
ηmax = %
4.Medium
TH​ = 400 °CTL​ = 5 °CEQH​ = 4000 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 5 °C. It takes in 4000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 5 °CQH = 4000 kJ
Wmax = kJ
5.Hard
TH​ = 700 °CT0​ = 27 °CTL​ = -15 °CERWQ̇H​ = 60 kWQ̇L​ = ?

A Carnot heat engine receives 60 kW of heat from a source at 700 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 700 °CT0 = 27 °CTL = -15 °CQ̇H = 60 kW
Q̇L = kW
6.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 0 °CQ̇H = 7 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 466.7 MW
  2. 2. η = 40 %
  3. 3. ηmax = 64.85 %
  4. 4. Wmax = 2347 kJ
  5. 5. Q̇L = 255 kW
  6. 6. Ẇmin = 0.4776 kW

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