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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 42%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 42%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 2800 kJQL​ = 1820 kJW = ?

A heat engine takes in 2800 kJ of heat from a hot reservoir and rejects 1820 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2800 kJQL = 1820 kJ
W = kJ
3.Medium
TH​ = 40 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 2 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 2 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = -10 °CTH = 40 °CQ̇L = 2 kW
Q̇H = kW
4.Medium
TH​ = 625 °CTL​ = 20 °CEQH​ = 2000 kJQL​W = ?

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 20 °C. It takes in 2000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 625 °CTL = 20 °CQH = 2000 kJ
Wmax = kJ
5.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 5 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 5 °CQ̇H = 8 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 0 °CHPQ̇H​ = 6 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is 0 °C outside, delivering 6 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = 0 °CQ̇H = 6 kW
COPmax =

Answer key

  1. 1. Q̇H = 1786 MW
  2. 2. W = 980 kJ
  3. 3. Q̇H = 2.38 kW
  4. 4. Wmax = 1347 kJ
  5. 5. Ẇmin = 0.4352 kW
  6. 6. COPmax = 13.42

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