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
kitchencold spaceRQ̇H​ = ?Q̇L​ = 9.46 kWẆ = 2.2 kW

A refrigerator removes heat from its cold space at a rate of 9.46 kW while its compressor uses 2.2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 9.46 kWẆ = 2.2 kW
Q̇H = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 45%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 45%
Q̇H = MW
3.Medium
TH​ = 325 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 35 °CTL​ = 2 °CRQ̇H​ = ?Q̇L​ = 10 kWẆ

A reversible refrigerator keeps a cold room at 2 °C by removing 10 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = 2 °CTH = 35 °CQ̇L = 10 kW
Q̇H = kW
5.Hard
TH​ = 32 °CTL​ = -25 °CRQ̇H​Q̇L​ = 3.5 kWẆ

A refrigerator keeps its cold space at -25 °C in a kitchen at 32 °C, removing heat from the cold space at 3.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = -25 °CQ̇L = 3.5 kW
COPmax =
6.Hard
TH​ = 550 °CTL​ = 40 °CEQH​ = 1200 kJQL​ = 600 kJW = 600 kJ

A heat engine takes in 1200 kJ of heat from a reservoir at 550 °C, produces 600 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 550 °CTL = 40 °CQH = 1200 kJW = 600 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇H = 11.66 kW
  2. 2. Q̇H = 1667 MW
  3. 3. ηmax = 51.83 %
  4. 4. Q̇H = 11.2 kW
  5. 5. COPmax = 4.354
  6. 6. Sgen = 0.4582 kJ/K

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