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​ = 800 kJQL​ = 560 kJW = ?

A heat engine takes in 800 kJ of heat from a hot reservoir and rejects 560 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 800 kJQL = 560 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 42%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 42%
Q̇L = MW
3.Medium
TH​ = 625 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 625 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 375 °CTL​ = 20 °CEQH​ = 4200 kJQL​W = ?

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 20 °C. It takes in 4200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 375 °CTL = 20 °CQH = 4200 kJ
Wmax = kJ
5.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 11 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 0 °CQ̇H = 11 kW
Ẇmin = kW
6.Hard
TH​ = 35 °CTL​ = -10 °CHPQ̇H​ = 8.5 kWQ̇L​Ẇ = ?

A heat pump delivers 8.5 kW of heat to a heating system at 35 °C, taking heat from a source at -10 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 35 °CTL = -10 °CηII = 45%Q̇H = 8.5 kW
Ẇ = kW

Answer key

  1. 1. W = 240 kJ
  2. 2. Q̇L = 69.05 MW
  3. 3. ηmax = 66.25 %
  4. 4. Wmax = 2300 kJ
  5. 5. Ẇmin = 0.7505 kW
  6. 6. Ẇ = 2.758 kW

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