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​ = 4300 kJQL​ = 3010 kJW = ?

A heat engine takes in 4300 kJ of heat from a hot reservoir and rejects 3010 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4300 kJQL = 3010 kJ
W = kJ
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 2.16 kWẆ = 1.2 kW

A refrigerator removes heat from its cold space at a rate of 2.16 kW while its compressor uses 1.2 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.16 kWẆ = 1.2 kW
COPR =
3.Medium
TH​ = 700 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 700 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 25 °CTL​ = 4 °CRQ̇H​ = ?Q̇L​ = 3.5 kWẆ

A reversible refrigerator keeps a cold room at 4 °C by removing 3.5 kW of heat, and rejects heat to the surroundings at 25 °C. Find the rate Q̇H at which it rejects heat.

TL = 4 °CTH = 25 °CQ̇L = 3.5 kW
Q̇H = kW
5.Hard
TH​ = 750 °CTL​ = 10 °CEQH​ = 2300 kJQL​ = 1311 kJW = 989 kJ

A heat engine takes in 2300 kJ of heat from a reservoir at 750 °C, produces 989 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 10 °CQH = 2300 kJW = 989 kJ
Sgen = kJ/K
6.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 15 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 15 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = 2 °CQ̇H = 15 kW
COPmax =

Answer key

  1. 1. W = 1290 kJ
  2. 2. COPR = 1.8
  3. 3. ηmax = 67.82 %
  4. 4. Q̇H = 3.765 kW
  5. 5. Sgen = 2.382 kJ/K
  6. 6. COPmax = 16.29

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