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​ = 2600 kJQL​ = 1690 kJW = ?

A heat engine takes in 2600 kJ of heat from a hot reservoir and rejects 1690 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2600 kJQL = 1690 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 5.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.1 delivers 5.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.1Q̇H = 5.5 kW
Q̇L = kW
3.Medium
TH​ = 225 °CTL​ = 20 °CEQH​ = 1600 kJQL​W = ?

A heat engine works between a hot reservoir at 225 °C and a cold reservoir at 20 °C. It takes in 1600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 225 °CTL = 20 °CQH = 1600 kJ
Wmax = kJ
4.Medium
TH​ = 475 °CTL​ = ?EQH​ = 3200 kJQL​ = 1232 kJW

A reversible (Carnot) heat engine takes in 3200 kJ of heat from a reservoir at 475 °C and rejects 1232 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 475 °CQH = 3200 kJQL = 1232 kJ
TL = °C
5.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 5 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 5 °CQ̇H = 14 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = -5 °CHPQ̇H​ = 4.5 kWQ̇L​Ẇ = ?

A heat pump delivers 4.5 kW of heat to a heating system at 22 °C, taking heat from a source at -5 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = -5 °CηII = 55%Q̇H = 4.5 kW
Ẇ = kW

Answer key

  1. 1. W = 910 kJ
  2. 2. Q̇L = 3.726 kW
  3. 3. Wmax = 658.4 kJ
  4. 4. TL = 14.89 °C
  5. 5. Ẇmin = 0.8064 kW
  6. 6. Ẇ = 0.7485 kW

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