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​ = 7 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.1 delivers 7 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.1Q̇H = 7 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 4700 kJQL​ = 3760 kJW = ?

A heat engine takes in 4700 kJ of heat from a hot reservoir and rejects 3760 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4700 kJQL = 3760 kJ
W = kJ
3.Medium
TH​ = 325 °CTL​ = 15 °CEQH​ = 2500 kJQL​W = ?

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 15 °C. It takes in 2500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 325 °CTL = 15 °CQH = 2500 kJ
Wmax = kJ
4.Medium
TH​ = 750 °CTL​ = 30 °CEQH​QL​η = 42%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 42%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 30 °Cη = 42%
ηII = %
5.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 3 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -10 °CQ̇L = 3 kW
Ẇmin = kW
6.Hard
TH​ = 28 °CTL​ = -20 °CRQ̇H​Q̇L​ = 5 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 28 °C, removing heat from the cold space at 5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = -20 °CQ̇L = 5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 5.293 kW
  2. 2. W = 940 kJ
  3. 3. Wmax = 1296 kJ
  4. 4. ηII = 59.68 %
  5. 5. Ẇmin = 0.4788 kW
  6. 6. Ẇmin = 0.9481 kW

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