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 40%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 1000 MWη = 40%
Q̇L = MW
2.Easy
houseoutside airHPQ̇H​ = 19 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.5 delivers 19 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.5Q̇H = 19 kW
Q̇L = kW
3.Medium
TH​ = 275 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 275 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 600 °CTL​ = 10 °CEQH​QL​η = 41%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 41%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 10 °Cη = 41%
ηII = %
5.Hard
TH​ = 500 °CTL​ = 10 °CEQH​ = 4500 kJQL​ = 2520 kJW = 1980 kJ

A heat engine takes in 4500 kJ of heat from a reservoir at 500 °C, produces 1980 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 500 °CTL = 10 °CQH = 4500 kJW = 1980 kJ
Sgen = kJ/K
6.Hard
TH​ = 500 °CT0​ = 27 °CTL​ = -25 °CERWQ̇H​ = 80 kWQ̇L​ = ?

A Carnot heat engine receives 80 kW of heat from a source at 500 °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 -25 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 500 °CT0 = 27 °CTL = -25 °CQ̇H = 80 kW
Q̇L = kW

Answer key

  1. 1. Q̇L = 1500 MW
  2. 2. Q̇L = 13.57 kW
  3. 3. ηmax = 44.7 %
  4. 4. ηII = 60.68 %
  5. 5. Sgen = 3.08 kJ/K
  6. 6. Q̇L = 233.6 kW

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