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​ = 1200 kJQL​ = 780 kJW = ?

A heat engine takes in 1200 kJ of heat from a hot reservoir and rejects 780 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1200 kJQL = 780 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 11.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.7 delivers 11.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.7Q̇H = 11.5 kW
Ẇ = kW
3.Medium
TH​ = 250 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 30 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 10 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 10 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = 0 °CTH = 30 °CQ̇L = 10 kW
Q̇H = kW
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 13.5 kWQ̇L​Ẇ = ?

A heat pump delivers 13.5 kW of heat to a heating system at 21 °C, taking heat from a source at -10 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -10 °CηII = 50%Q̇H = 13.5 kW
Ẇ = kW
6.Hard
TH​ = 30 °CTL​ = 5 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 30 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 5 °CQ̇L = 4 kW
Ẇmin = kW

Answer key

  1. 1. W = 420 kJ
  2. 2. Ẇ = 2.447 kW
  3. 3. ηmax = 40.14 %
  4. 4. Q̇H = 11.1 kW
  5. 5. Ẇ = 2.845 kW
  6. 6. Ẇmin = 0.3595 kW

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