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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Name: ____________________   Date: ____________

1.Easy
kitchencold spaceRQ̇H​Q̇L​ = 0.64 kWẆ = 0.4 kW

A refrigerator removes heat from its cold space at a rate of 0.64 kW while its compressor uses 0.4 kW of power. Find its coefficient of performance COPR.

Q̇L = 0.64 kWẆ = 0.4 kW
COPR =
2.Easy
houseoutside airHPQ̇H​ = 12.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.1 delivers 12.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.1Q̇H = 12.5 kW
Ẇ = kW
3.Medium
TH​ = 575 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 575 °CTL = 25 °C
ηmax = %
4.Medium
TH​ = 200 °CTL​ = 35 °CEQH​ = 3000 kJQL​W = ?

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 35 °C. It takes in 3000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 200 °CTL = 35 °CQH = 3000 kJ
Wmax = kJ
5.Hard
TH​ = 400 °CT0​ = 27 °CTL​ = -5 °CERWQ̇H​ = 150 kWQ̇L​ = ?

A Carnot heat engine receives 150 kW of heat from a source at 400 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -5 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 400 °CT0 = 27 °CTL = -5 °CQ̇H = 150 kW
Q̇L = kW
6.Hard
TH​ = 28 °CTL​ = -10 °CRQ̇H​Q̇L​ = 1.5 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 28 °C, removing heat from the cold space at 1.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = -10 °CQ̇L = 1.5 kW
COPmax =

Answer key

  1. 1. COPR = 1.6
  2. 2. Ẇ = 3.049 kW
  3. 3. ηmax = 64.85 %
  4. 4. Wmax = 1046 kJ
  5. 5. Q̇L = 696.5 kW
  6. 6. COPmax = 6.925

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