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​ = 10.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.2 delivers 10.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.2Q̇H = 10.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 2400 kJQL​ = 1440 kJW = ?

A heat engine takes in 2400 kJ of heat from a hot reservoir and rejects 1440 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2400 kJQL = 1440 kJ
W = kJ
3.Medium
TH​ = 40 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 7.5 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 7.5 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 40 °CQ̇L = 7.5 kW
Q̇H = kW
4.Medium
TH​ = 800 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 20 °C
ηmax = %
5.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 19 kWQ̇L​Ẇ = ?

A heat pump delivers 19 kW of heat to a heating system at 20 °C, taking heat from a source at 7 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = 7 °CηII = 30%Q̇H = 19 kW
Ẇ = kW
6.Hard
TH​ = 25 °CTL​ = 2 °CRQ̇H​Q̇L​ = 4.5 kWẆ

A refrigerator keeps its cold space at 2 °C in a kitchen at 25 °C, removing heat from the cold space at 4.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 25 °CTL = 2 °CQ̇L = 4.5 kW
COPmax =

Answer key

  1. 1. Q̇L = 7.219 kW
  2. 2. W = 960 kJ
  3. 3. Q̇H = 9.278 kW
  4. 4. ηmax = 72.68 %
  5. 5. Ẇ = 2.809 kW
  6. 6. COPmax = 11.96

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