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​ = 3000 kJQL​ = 2250 kJW = ?

A heat engine takes in 3000 kJ of heat from a hot reservoir and rejects 2250 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3000 kJQL = 2250 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.8 delivers 10 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.8Q̇H = 10 kW
Ẇ = kW
3.Medium
TH​ = 900 °CTL​ = 30 °CEQH​QL​η = 56%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 56%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 30 °Cη = 56%
ηII = %
4.Medium
TH​ = 28 °CTL​ = -5 °CRQ̇H​ = ?Q̇L​ = 8 kWẆ

A reversible refrigerator keeps a cold room at -5 °C by removing 8 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -5 °CTH = 28 °CQ̇L = 8 kW
Q̇H = kW
5.Hard
TH​ = 300 °CTL​ = 25 °CEQH​ = 3700 kJQL​ = 2442 kJW = 1258 kJ

A heat engine takes in 3700 kJ of heat from a reservoir at 300 °C, produces 1258 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 300 °CTL = 25 °CQH = 3700 kJW = 1258 kJ
Sgen = kJ/K
6.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 6 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 6 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = 2 °CQ̇H = 6 kW
COPmax =

Answer key

  1. 1. W = 750 kJ
  2. 2. Ẇ = 2.083 kW
  3. 3. ηII = 75.51 %
  4. 4. Q̇H = 8.985 kW
  5. 5. Sgen = 1.735 kJ/K
  6. 6. COPmax = 16.29

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