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​ = 4900 kJQL​ = 3920 kJW = ?

A heat engine takes in 4900 kJ of heat from a hot reservoir and rejects 3920 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4900 kJQL = 3920 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 40%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 150 MWη = 40%
Q̇L = MW
3.Medium
TH​ = 200 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 200 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 450 °CTL​ = 15 °CEQH​ = 2000 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 15 °C. It takes in 2000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 15 °CQH = 2000 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -10 °CQ̇H = 7 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 0 °CHPQ̇H​ = 5 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 0 °C outside, delivering 5 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 0 °CQ̇H = 5 kW
Ẇmin = kW

Answer key

  1. 1. W = 980 kJ
  2. 2. Q̇L = 225 MW
  3. 3. ηmax = 34.87 %
  4. 4. Wmax = 1203 kJ
  5. 5. Ẇmin = 0.7589 kW
  6. 6. Ẇmin = 0.3727 kW

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