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
hot reservoircold reservoirEQH​ = 3500 kJQL​ = 2450 kJW

A heat engine takes in 3500 kJ of heat from a hot reservoir and rejects 2450 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3500 kJQL = 2450 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 7 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4 delivers 7 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4Q̇H = 7 kW
Q̇L = kW
3.Medium
TH​ = 400 °CTL​ = 15 °CEQH​QL​η = 23%

A heat engine receives heat from a source at 400 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 23%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 400 °CTL = 15 °Cη = 23%
ηII = %
4.Medium
TH​ = 25 °CTL​ = 4 °CRQ̇H​ = ?Q̇L​ = 9 kWẆ

A reversible refrigerator keeps a cold room at 4 °C by removing 9 kW of heat, and rejects heat to the surroundings at 25 °C. Find the rate Q̇H at which it rejects heat.

TL = 4 °CTH = 25 °CQ̇L = 9 kW
Q̇H = kW
5.Hard
TH​ = 400 °CTL​ = 25 °CEQH​ = 2900 kJQL​ = 2088 kJW = 812 kJ

A heat engine takes in 2900 kJ of heat from a reservoir at 400 °C, produces 812 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 400 °CTL = 25 °CQH = 2900 kJW = 812 kJ
Sgen = kJ/K
6.Hard
TH​ = 700 °CTL​ = 15 °CEQH​ = 4000 kJQL​ = 2600 kJW = 1400 kJ

A heat engine takes in 4000 kJ of heat from a reservoir at 700 °C, produces 1400 kJ of work and rejects the rest to a reservoir at 15 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 700 °CTL = 15 °CQH = 4000 kJW = 1400 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 30 %
  2. 2. Q̇L = 5.25 kW
  3. 3. ηII = 40.21 %
  4. 4. Q̇H = 9.682 kW
  5. 5. Sgen = 2.695 kJ/K
  6. 6. Sgen = 4.913 kJ/K

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