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​ = 3900 kJQL​ = 2730 kJW = ?

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2730 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3900 kJQL = 2730 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4400 kJQL​ = 3080 kJW = ?

A heat engine takes in 4400 kJ of heat from a hot reservoir and rejects 3080 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4400 kJQL = 3080 kJ
W = kJ
3.Medium
TH​ = 625 °CTL​ = ?EQH​ = 1000 kJQL​ = 326 kJW

A reversible (Carnot) heat engine takes in 1000 kJ of heat from a reservoir at 625 °C and rejects 326 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 625 °CQH = 1000 kJQL = 326 kJ
TL = °C
4.Medium
TH​ = 675 °CTL​ = ?EQH​ = 2300 kJQL​ = 760 kJW

A reversible (Carnot) heat engine takes in 2300 kJ of heat from a reservoir at 675 °C and rejects 760 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 675 °CQH = 2300 kJQL = 760 kJ
TL = °C
5.Hard
TH​ = 55 °CTL​ = 10 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump delivers 9 kW of heat to a heating system at 55 °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 = 55 °CTL = 10 °CηII = 30%Q̇H = 9 kW
Ẇ = kW
6.Hard
TH​ = 400 °CT0​ = 30 °CTL​ = -15 °CERWQ̇H​ = 180 kWQ̇L​ = ?

A Carnot heat engine receives 180 kW of heat from a source at 400 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 400 °CT0 = 30 °CTL = -15 °CQ̇H = 180 kW
Q̇L = kW

Answer key

  1. 1. W = 1170 kJ
  2. 2. W = 1320 kJ
  3. 3. TL = 19.65 °C
  4. 4. TL = 40.15 °C
  5. 5. Ẇ = 4.114 kW
  6. 6. Q̇L = 567.6 kW

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