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​ = 11.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.4 delivers 11.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.4Q̇H = 11.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 900 kJQL​ = 495 kJW = ?

A heat engine takes in 900 kJ of heat from a hot reservoir and rejects 495 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 900 kJQL = 495 kJ
W = kJ
3.Medium
TH​ = 300 °CTL​ = 10 °CEQH​QL​η = 30%

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 30%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 10 °Cη = 30%
ηII = %
4.Medium
TH​ = 550 °CTL​ = 30 °CEQH​QL​η = 35%

A heat engine receives heat from a source at 550 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 35%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 550 °CTL = 30 °Cη = 35%
ηII = %
5.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -10 °CQ̇L = 3.5 kW
Ẇmin = kW
6.Hard
TH​ = 35 °CTL​ = 4 °CRQ̇H​Q̇L​ = 2.5 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 35 °C, removing heat from the cold space at 2.5 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = 4 °CQ̇L = 2.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 8.118 kW
  2. 2. W = 405 kJ
  3. 3. ηII = 59.29 %
  4. 4. ηII = 55.4 %
  5. 5. Ẇmin = 0.5586 kW
  6. 6. Ẇmin = 0.2796 kW

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