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​ = 4900 kJQL​ = 2695 kJW = ?

A heat engine takes in 4900 kJ of heat from a hot reservoir and rejects 2695 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4900 kJQL = 2695 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.6 delivers 10 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.6Q̇H = 10 kW
Ẇ = kW
3.Medium
TH​ = 28 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 6.5 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 6.5 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 28 °CQ̇L = 6.5 kW
Q̇H = kW
4.Medium
TH​ = 675 °CTL​ = ?EQH​ = 1800 kJQL​ = 613 kJW

A reversible (Carnot) heat engine takes in 1800 kJ of heat from a reservoir at 675 °C and rejects 613 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 675 °CQH = 1800 kJQL = 613 kJ
TL = °C
5.Hard
TH​ = 22 °CTL​ = -5 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump delivers 6 kW of heat to a heating system at 22 °C, taking heat from a source at -5 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = -5 °CηII = 45%Q̇H = 6 kW
Ẇ = kW
6.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 15 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 15 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = 2 °CQ̇H = 15 kW
COPmax =

Answer key

  1. 1. W = 2205 kJ
  2. 2. Ẇ = 3.846 kW
  3. 3. Q̇H = 7.732 kW
  4. 4. TL = 49.75 °C
  5. 5. Ẇ = 1.22 kW
  6. 6. COPmax = 16.29

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