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​ = 3100 kJQL​ = 1860 kJW = ?

A heat engine takes in 3100 kJ of heat from a hot reservoir and rejects 1860 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3100 kJQL = 1860 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 6.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.1 delivers 6.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.1Q̇H = 6.5 kW
Q̇L = kW
3.Medium
TH​ = 30 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 7.5 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 7.5 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = -10 °CTH = 30 °CQ̇L = 7.5 kW
Q̇H = kW
4.Medium
TH​ = 750 °CTL​ = 25 °CEQH​ = 2500 kJQL​W = ?

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 25 °C. It takes in 2500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 750 °CTL = 25 °CQH = 2500 kJ
Wmax = kJ
5.Hard
TH​ = 21 °CTL​ = 0 °CHPQ̇H​ = 5 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 0 °C outside, delivering 5 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 0 °CQ̇H = 5 kW
COPmax =
6.Hard
TH​ = 35 °CTL​ = -25 °CRQ̇H​Q̇L​ = 2 kWẆ

A refrigerator keeps its cold space at -25 °C in a kitchen at 35 °C, removing heat from the cold space at 2 kW. Find the highest possible coefficient of performance COPmax.

TH = 35 °CTL = -25 °CQ̇L = 2 kW
COPmax =

Answer key

  1. 1. W = 1240 kJ
  2. 2. Q̇L = 4.403 kW
  3. 3. Q̇H = 8.64 kW
  4. 4. Wmax = 1771 kJ
  5. 5. COPmax = 14.01
  6. 6. COPmax = 4.136

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