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​ = 5000 kJQL​ = 3250 kJW = ?

A heat engine takes in 5000 kJ of heat from a hot reservoir and rejects 3250 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 5000 kJQL = 3250 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 8 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.4 delivers 8 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.4Q̇H = 8 kW
Q̇L = kW
3.Medium
TH​ = 300 °CTL​ = 30 °CEQH​QL​η = 31%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 31%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 30 °Cη = 31%
ηII = %
4.Medium
TH​ = 725 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 725 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 725 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 30 °CTL​ = -25 °CRQ̇H​Q̇L​ = 0.5 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 30 °C, removing heat from the cold space at 0.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -25 °CQ̇L = 0.5 kW
Ẇmin = kW
6.Hard
TH​ = 300 °CTL​ = 15 °CEQH​ = 1800 kJQL​ = 1080 kJW = 720 kJ

A heat engine takes in 1800 kJ of heat from a reservoir at 300 °C, produces 720 kJ of work and rejects the rest to a reservoir at 15 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 300 °CTL = 15 °CQH = 1800 kJW = 720 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 1750 kJ
  2. 2. Q̇L = 5.647 kW
  3. 3. ηII = 65.81 %
  4. 4. ηmax = 72.13 %
  5. 5. Ẇmin = 0.1108 kW
  6. 6. Sgen = 0.6075 kJ/K

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