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​ = 9.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.2 delivers 9.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.2Q̇H = 9.5 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 3900 kJQL​ = 2730 kJW

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2730 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3900 kJQL = 2730 kJ
η = %
3.Medium
TH​ = 800 °CTL​ = 35 °CEQH​QL​η = 36%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 36%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 35 °Cη = 36%
ηII = %
4.Medium
TH​ = 550 °CTL​ = 40 °CEQH​QL​η = 25%

A heat engine receives heat from a source at 550 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 25%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 550 °CTL = 40 °Cη = 25%
ηII = %
5.Hard
TH​ = 600 °CTL​ = 40 °CEQH​ = 1400 kJQL​ = 770 kJW = 630 kJ

A heat engine takes in 1400 kJ of heat from a reservoir at 600 °C, produces 630 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 600 °CTL = 40 °CQH = 1400 kJW = 630 kJ
Sgen = kJ/K
6.Hard
TH​ = 950 °CT0​ = 25 °CTL​ = -15 °CERWQ̇H​ = 200 kWQ̇L​ = ?

A Carnot heat engine receives 200 kW of heat from a source at 950 °C and rejects heat to the surroundings at 25 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 950 °CT0 = 25 °CTL = -15 °CQ̇H = 200 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 2.969 kW
  2. 2. η = 30 %
  3. 3. ηII = 50.5 %
  4. 4. ηII = 40.35 %
  5. 5. Sgen = 0.8555 kJ/K
  6. 6. Q̇L = 976.1 kW

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