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​ = 600 kJQL​ = 450 kJW

A heat engine takes in 600 kJ of heat from a hot reservoir and rejects 450 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 600 kJQL = 450 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 150 MWη = 42%
Q̇L = MW
3.Medium
TH​ = 650 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 650 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 325 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 20 °C
ηmax = %
5.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 7 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 7 °CQ̇H = 8 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -10 °CQ̇H = 14 kW
Ẇmin = kW

Answer key

  1. 1. η = 25 %
  2. 2. Q̇L = 207.1 MW
  3. 3. ηmax = 66.62 %
  4. 4. ηmax = 50.99 %
  5. 5. Ẇmin = 0.3808 kW
  6. 6. Ẇmin = 1.518 kW

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