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​ = 12.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 2.8 delivers 12.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 2.8Q̇H = 12.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 2900 kJQL​ = 2320 kJW

A heat engine takes in 2900 kJ of heat from a hot reservoir and rejects 2320 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2900 kJQL = 2320 kJ
η = %
3.Medium
TH​ = 750 °CTL​ = 15 °CEQH​ = 3900 kJQL​W = ?

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 15 °C. It takes in 3900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 750 °CTL = 15 °CQH = 3900 kJ
Wmax = kJ
4.Medium
TH​ = 700 °CTL​ = ?EQH​ = 4400 kJQL​ = 1461 kJW

A reversible (Carnot) heat engine takes in 4400 kJ of heat from a reservoir at 700 °C and rejects 1461 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 700 °CQH = 4400 kJQL = 1461 kJ
TL = °C
5.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 7 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 7 °CQ̇H = 14 kW
Ẇmin = kW
6.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 18.5 kWQ̇L​Ẇ = ?

A heat pump delivers 18.5 kW of heat to a heating system at 21 °C, taking heat from a source at 2 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = 2 °CηII = 55%Q̇H = 18.5 kW
Ẇ = kW

Answer key

  1. 1. Q̇L = 8.036 kW
  2. 2. η = 20 %
  3. 3. Wmax = 2802 kJ
  4. 4. TL = 49.98 °C
  5. 5. Ẇmin = 0.6663 kW
  6. 6. Ẇ = 2.173 kW

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