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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Name: ____________________   Date: ____________

1.Easy
houseoutside airHPQ̇H​ = 11.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 2.9 delivers 11.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 2.9Q̇H = 11.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 3900 kJQL​ = 2340 kJW = ?

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2340 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3900 kJQL = 2340 kJ
W = kJ
3.Medium
TH​ = 650 °CTL​ = ?EQH​ = 4100 kJQL​ = 1435 kJW

A reversible (Carnot) heat engine takes in 4100 kJ of heat from a reservoir at 650 °C and rejects 1435 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 650 °CQH = 4100 kJQL = 1435 kJ
TL = °C
4.Medium
TH​ = 200 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 200 °CTL = 10 °C
ηmax = %
5.Hard
TH​ = 21 °CTL​ = -5 °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 -5 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -5 °CηII = 45%Q̇H = 13.5 kW
Ẇ = kW
6.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 15 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 7.534 kW
  2. 2. W = 1560 kJ
  3. 3. TL = 49.95 °C
  4. 4. ηmax = 40.16 %
  5. 5. Ẇ = 2.652 kW
  6. 6. Ẇmin = 1.016 kW

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