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 = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 30%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 600 MWη = 30%
Q̇L = MW
2.Easy
hot reservoircold reservoirEQH​ = 1400 kJQL​ = 770 kJW

A heat engine takes in 1400 kJ of heat from a hot reservoir and rejects 770 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1400 kJQL = 770 kJ
η = %
3.Medium
TH​ = 650 °CTL​ = 35 °CEQH​ = 1100 kJQL​W = ?

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 35 °C. It takes in 1100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 650 °CTL = 35 °CQH = 1100 kJ
Wmax = kJ
4.Medium
TH​ = 550 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 550 °CTL = 35 °C
ηmax = %
5.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 2 °CQ̇H = 7 kW
Ẇmin = kW
6.Hard
TH​ = 900 °CTL​ = 15 °CEQH​ = 1400 kJQL​ = 658 kJW = 742 kJ

A heat engine takes in 1400 kJ of heat from a reservoir at 900 °C, produces 742 kJ of work and rejects the rest to a reservoir at 15 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 900 °CTL = 15 °CQH = 1400 kJW = 742 kJ
Sgen = kJ/K

Answer key

  1. 1. Q̇L = 1400 MW
  2. 2. η = 45 %
  3. 3. Wmax = 732.8 kJ
  4. 4. ηmax = 62.56 %
  5. 5. Ẇmin = 0.4522 kW
  6. 6. Sgen = 1.09 kJ/K

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