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 45%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 1000 MWη = 45%
Q̇H = MW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 1.12 kWẆ = 0.7 kW

A refrigerator removes heat from its cold space at a rate of 1.12 kW while its compressor uses 0.7 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 1.12 kWẆ = 0.7 kW
Q̇H = kW
3.Medium
TH​ = 775 °CTL​ = ?EQH​ = 5000 kJQL​ = 1518 kJW

A reversible (Carnot) heat engine takes in 5000 kJ of heat from a reservoir at 775 °C and rejects 1518 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 775 °CQH = 5000 kJQL = 1518 kJ
TL = °C
4.Medium
TH​ = 300 °CTL​ = 35 °CEQH​QL​η = 32%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 32%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 35 °Cη = 32%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 8 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 8 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 7 °CQ̇H = 8 kW
COPmax =
6.Hard
TH​ = 400 °CTL​ = 20 °CEQH​ = 2400 kJQL​ = 1440 kJW = 960 kJ

A heat engine takes in 2400 kJ of heat from a reservoir at 400 °C, produces 960 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 400 °CTL = 20 °CQH = 2400 kJW = 960 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇H = 2222 MW
  2. 2. Q̇H = 1.82 kW
  3. 3. TL = 45.07 °C
  4. 4. ηII = 69.21 %
  5. 5. COPmax = 19.68
  6. 6. Sgen = 1.347 kJ/K

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