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​ = 1.44 kWẆ = 0.6 kW

A refrigerator removes heat from its cold space at a rate of 1.44 kW while its compressor uses 0.6 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 1.44 kWẆ = 0.6 kW
Q̇H = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 42%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 50 MWη = 42%
Q̇H = MW
3.Medium
TH​ = 500 °CTL​ = 5 °CEQH​ = 1700 kJQL​W = ?

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 5 °C. It takes in 1700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 500 °CTL = 5 °CQH = 1700 kJ
Wmax = kJ
4.Medium
TH​ = 300 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 300 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 300 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 25 °CTL​ = -25 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 25 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = -25 °CQ̇L = 1.5 kW
Ẇmin = kW
6.Hard
TH​ = 550 °CTL​ = 40 °CEQH​ = 500 kJQL​ = 285 kJW = 215 kJ

A heat engine takes in 500 kJ of heat from a reservoir at 550 °C, produces 215 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 = 500 kJW = 215 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇H = 2.04 kW
  2. 2. Q̇H = 119 MW
  3. 3. Wmax = 1088 kJ
  4. 4. ηmax = 51.47 %
  5. 5. Ẇmin = 0.3022 kW
  6. 6. Sgen = 0.3027 kJ/K

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