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​ = 20 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.6 delivers 20 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.6Q̇H = 20 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 3600 kJQL​ = 2700 kJW = ?

A heat engine takes in 3600 kJ of heat from a hot reservoir and rejects 2700 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3600 kJQL = 2700 kJ
W = kJ
3.Medium
TH​ = 325 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 325 °CTL​ = 20 °CEQH​ = 1900 kJQL​W = ?

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 20 °C. It takes in 1900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 325 °CTL = 20 °CQH = 1900 kJ
Wmax = kJ
5.Hard
TH​ = 600 °CT0​ = 25 °CTL​ = -5 °CERWQ̇H​ = 20 kWQ̇L​ = ?

A Carnot heat engine receives 20 kW of heat from a source at 600 °C and rejects heat to the surroundings at 25 °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 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 600 °CT0 = 25 °CTL = -5 °CQ̇H = 20 kW
Q̇L = kW
6.Hard
TH​ = 55 °CTL​ = 2 °CHPQ̇H​ = 12.5 kWQ̇L​Ẇ = ?

A heat pump delivers 12.5 kW of heat to a heating system at 55 °C, taking heat from a source at 2 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 2 °CηII = 35%Q̇H = 12.5 kW
Ẇ = kW

Answer key

  1. 1. Q̇L = 14.44 kW
  2. 2. W = 900 kJ
  3. 3. ηmax = 53.5 %
  4. 4. Wmax = 968.8 kJ
  5. 5. Q̇L = 117.7 kW
  6. 6. Ẇ = 5.768 kW

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