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
houseoutside airHPQ̇H​ = 5.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.9 delivers 5.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.9Q̇H = 5.5 kW
Q̇L = kW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 9.88 kWẆ = 2.6 kW

A refrigerator removes heat from its cold space at a rate of 9.88 kW while its compressor uses 2.6 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 9.88 kWẆ = 2.6 kW
Q̇H = kW
3.Medium
TH​ = 375 °CTL​ = 40 °CEQH​ = 3500 kJQL​W = ?

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 40 °C. It takes in 3500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 375 °CTL = 40 °CQH = 3500 kJ
Wmax = kJ
4.Medium
TH​ = 775 °CTL​ = 25 °CEQH​ = 4400 kJQL​W = ?

A heat engine works between a hot reservoir at 775 °C and a cold reservoir at 25 °C. It takes in 4400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 775 °CTL = 25 °CQH = 4400 kJ
Wmax = kJ
5.Hard
TH​ = 750 °CTL​ = 20 °CEQH​ = 3300 kJQL​ = 2112 kJW = 1188 kJ

A heat engine takes in 3300 kJ of heat from a reservoir at 750 °C, produces 1188 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 20 °CQH = 3300 kJW = 1188 kJ
Sgen = kJ/K
6.Hard
TH​ = 25 °CTL​ = 5 °CRQ̇H​Q̇L​ = 2.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 25 °C, removing heat from the cold space at 2.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 5 °CQ̇L = 2.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 4.378 kW
  2. 2. Q̇H = 12.48 kW
  3. 3. Wmax = 1809 kJ
  4. 4. Wmax = 3148 kJ
  5. 5. Sgen = 3.979 kJ/K
  6. 6. Ẇmin = 0.1798 kW

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