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​ = 19 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.9 delivers 19 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.9Q̇H = 19 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 1700 kJQL​ = 935 kJW

A heat engine takes in 1700 kJ of heat from a hot reservoir and rejects 935 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1700 kJQL = 935 kJ
η = %
3.Medium
TH​ = 450 °CTL​ = 40 °CEQH​ = 3800 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 40 °C. It takes in 3800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 40 °CQH = 3800 kJ
Wmax = kJ
4.Medium
TH​ = 700 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 700 °CTL = 25 °C
ηmax = %
5.Hard
TH​ = 30 °CTL​ = 4 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 4 °CQ̇L = 1.5 kW
Ẇmin = kW
6.Hard
TH​ = 32 °CTL​ = 4 °CRQ̇H​Q̇L​ = 0.5 kWẆ

A refrigerator keeps its cold space at 4 °C in a kitchen at 32 °C, removing heat from the cold space at 0.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = 4 °CQ̇L = 0.5 kW
COPmax =

Answer key

  1. 1. Ẇ = 3.878 kW
  2. 2. η = 45 %
  3. 3. Wmax = 2154 kJ
  4. 4. ηmax = 69.36 %
  5. 5. Ẇmin = 0.1407 kW
  6. 6. COPmax = 9.898

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