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​ = 4800 kJQL​ = 2640 kJW

A heat engine takes in 4800 kJ of heat from a hot reservoir and rejects 2640 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4800 kJQL = 2640 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 17 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 2.7 delivers 17 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 2.7Q̇H = 17 kW
Q̇L = kW
3.Medium
TH​ = 475 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 475 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 475 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 350 °CTL​ = 35 °CEQH​ = 2700 kJQL​W = ?

A heat engine works between a hot reservoir at 350 °C and a cold reservoir at 35 °C. It takes in 2700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 350 °CTL = 35 °CQH = 2700 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 10 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 10 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 7 °CQ̇H = 10 kW
COPmax =
6.Hard
TH​ = 28 °CTL​ = -25 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 28 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = -25 °CQ̇L = 1.5 kW
Ẇmin = kW

Answer key

  1. 1. η = 45 %
  2. 2. Q̇L = 10.7 kW
  3. 3. ηmax = 58.14 %
  4. 4. Wmax = 1365 kJ
  5. 5. COPmax = 19.68
  6. 6. Ẇmin = 0.3204 kW

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