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​ = 3600 kJQL​ = 2340 kJW

A heat engine takes in 3600 kJ of heat from a hot reservoir and rejects 2340 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3600 kJQL = 2340 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 2300 kJQL​ = 1495 kJW

A heat engine takes in 2300 kJ of heat from a hot reservoir and rejects 1495 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2300 kJQL = 1495 kJ
η = %
3.Medium
TH​ = 800 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 325 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 10 °C
ηmax = %
5.Hard
TH​ = 35 °CTL​ = 10 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump delivers 6 kW of heat to a heating system at 35 °C, taking heat from a source at 10 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 35 °CTL = 10 °CηII = 30%Q̇H = 6 kW
Ẇ = kW
6.Hard
TH​ = 600 °CT0​ = 20 °CTL​ = -20 °CERWQ̇H​ = 70 kWQ̇L​ = ?

A Carnot heat engine receives 70 kW of heat from a source at 600 °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 -20 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 600 °CT0 = 20 °CTL = -20 °CQ̇H = 70 kW
Q̇L = kW

Answer key

  1. 1. η = 35 %
  2. 2. η = 35 %
  3. 3. ηmax = 71.75 %
  4. 4. ηmax = 52.66 %
  5. 5. Ẇ = 1.623 kW
  6. 6. Q̇L = 294.3 kW

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