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​ = 3300 kJQL​ = 2145 kJW

A heat engine takes in 3300 kJ of heat from a hot reservoir and rejects 2145 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3300 kJQL = 2145 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 3800 kJQL​ = 3040 kJW = ?

A heat engine takes in 3800 kJ of heat from a hot reservoir and rejects 3040 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3800 kJQL = 3040 kJ
W = kJ
3.Medium
TH​ = 600 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 600 °CTL = 25 °C
ηmax = %
4.Medium
TH​ = 250 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 35 °C
ηmax = %
5.Hard
TH​ = 800 °CT0​ = 20 °CTL​ = -5 °CERWQ̇H​ = 60 kWQ̇L​ = ?

A Carnot heat engine receives 60 kW of heat from a source at 800 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -5 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 800 °CT0 = 20 °CTL = -5 °CQ̇H = 60 kW
Q̇L = kW
6.Hard
TH​ = 35 °CTL​ = 0 °CHPQ̇H​ = 20 kWQ̇L​Ẇ = ?

A heat pump delivers 20 kW of heat to a heating system at 35 °C, taking heat from a source at 0 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 35 °CTL = 0 °CηII = 60%Q̇H = 20 kW
Ẇ = kW

Answer key

  1. 1. η = 35 %
  2. 2. W = 760 kJ
  3. 3. ηmax = 65.85 %
  4. 4. ηmax = 41.1 %
  5. 5. Q̇L = 467.8 kW
  6. 6. Ẇ = 3.786 kW

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