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​ = 14.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.5 delivers 14.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.5Q̇H = 14.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 3800 kJQL​ = 2090 kJW

A heat engine takes in 3800 kJ of heat from a hot reservoir and rejects 2090 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3800 kJQL = 2090 kJ
η = %
3.Medium
TH​ = 300 °CTL​ = 10 °CEQH​QL​η = 38%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 38%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 10 °Cη = 38%
ηII = %
4.Medium
TH​ = 20 °CTL​ = 5 °CRQ̇H​ = ?Q̇L​ = 4 kWẆ

A reversible refrigerator keeps a cold room at 5 °C by removing 4 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = 5 °CTH = 20 °CQ̇L = 4 kW
Q̇H = kW
5.Hard
650 °CTm​ = ?20 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 650 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 20 °C. Both engines produce the same work. Find Tm in °C.

TH = 650 °CTL = 20 °C
Tm = °C
6.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 7 °CQ̇H = 6 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 11.28 kW
  2. 2. η = 45 %
  3. 3. ηII = 75.1 %
  4. 4. Q̇H = 4.216 kW
  5. 5. Tm = 335 °C
  6. 6. Ẇmin = 0.3049 kW

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