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​ = 1.53 kWẆ = 0.9 kW

A refrigerator removes heat from its cold space at a rate of 1.53 kW while its compressor uses 0.9 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 1.53 kWẆ = 0.9 kW
Q̇H = kW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 2.31 kWẆ = 1.1 kW

A refrigerator removes heat from its cold space at a rate of 2.31 kW while its compressor uses 1.1 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.31 kWẆ = 1.1 kW
COPR =
3.Medium
TH​ = 28 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 1 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 1 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = 0 °CTH = 28 °CQ̇L = 1 kW
Q̇H = kW
4.Medium
TH​ = 475 °CTL​ = ?EQH​ = 4100 kJQL​ = 1497 kJW

A reversible (Carnot) heat engine takes in 4100 kJ of heat from a reservoir at 475 °C and rejects 1497 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 475 °CQH = 4100 kJQL = 1497 kJ
TL = °C
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -10 °CQ̇H = 15 kW
Ẇmin = kW
6.Hard
TH​ = 850 °CTL​ = 30 °CEQH​ = 1600 kJQL​ = 672 kJW = 928 kJ

A heat engine takes in 1600 kJ of heat from a reservoir at 850 °C, produces 928 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 850 °CTL = 30 °CQH = 1600 kJW = 928 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇H = 2.43 kW
  2. 2. COPR = 2.1
  3. 3. Q̇H = 1.103 kW
  4. 4. TL = 0.01599 °C
  5. 5. Ẇmin = 1.581 kW
  6. 6. Sgen = 0.7922 kJ/K

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