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​ = 4400 kJQL​ = 2420 kJW = ?

A heat engine takes in 4400 kJ of heat from a hot reservoir and rejects 2420 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4400 kJQL = 2420 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 16 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.6 delivers 16 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.6Q̇H = 16 kW
Ẇ = kW
3.Medium
TH​ = 20 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 8.5 kWẆ

A reversible refrigerator keeps a cold room at -25 °C by removing 8.5 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -25 °CTH = 20 °CQ̇L = 8.5 kW
Q̇H = kW
4.Medium
TH​ = 625 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 625 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 20 °CTL​ = 5 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 5 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 5 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 35 °CTL​ = 4 °CRQ̇H​Q̇L​ = 1 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 35 °C, removing heat from the cold space at 1 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = 4 °CQ̇L = 1 kW
Ẇmin = kW

Answer key

  1. 1. W = 1980 kJ
  2. 2. Ẇ = 6.154 kW
  3. 3. Q̇H = 10.04 kW
  4. 4. ηmax = 69.03 %
  5. 5. Ẇmin = 0.5117 kW
  6. 6. Ẇmin = 0.1119 kW

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