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 40%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 500 MWη = 40%
Q̇H = MW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 55%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 300 MWη = 55%
Q̇H = MW
3.Medium
TH​ = 400 °CTL​ = 40 °CEQH​ = 1600 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 40 °C. It takes in 1600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 40 °CQH = 1600 kJ
Wmax = kJ
4.Medium
TH​ = 325 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 40 °C
ηmax = %
5.Hard
TH​ = 850 °CT0​ = 25 °CTL​ = -20 °CERWQ̇H​ = 180 kWQ̇L​ = ?

A Carnot heat engine receives 180 kW of heat from a source at 850 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -20 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 850 °CT0 = 25 °CTL = -20 °CQ̇H = 180 kW
Q̇L = kW
6.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 14 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 14 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = -10 °CQ̇H = 14 kW
COPmax =

Answer key

  1. 1. Q̇H = 1250 MW
  2. 2. Q̇H = 545.5 MW
  3. 3. Wmax = 855.7 kJ
  4. 4. ηmax = 47.65 %
  5. 5. Q̇L = 743.8 kW
  6. 6. COPmax = 9.223

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