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​ = 900 kJQL​ = 585 kJW

A heat engine takes in 900 kJ of heat from a hot reservoir and rejects 585 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 900 kJQL = 585 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 38%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 38%
Q̇L = MW
3.Medium
TH​ = 250 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 475 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 475 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 475 °CTL = 15 °C
ηmax = %
5.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 4 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 4 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -5 °CQ̇H = 4 kW
Ẇmin = kW
6.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -10 °CQ̇H = 7 kW
Ẇmin = kW

Answer key

  1. 1. η = 35 %
  2. 2. Q̇L = 326.3 MW
  3. 3. ηmax = 43.96 %
  4. 4. ηmax = 61.48 %
  5. 5. Ẇmin = 0.3536 kW
  6. 6. Ẇmin = 0.7164 kW

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