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​ = 4700 kJQL​ = 3525 kJW = ?

A heat engine takes in 4700 kJ of heat from a hot reservoir and rejects 3525 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4700 kJQL = 3525 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 2900 kJQL​ = 1740 kJW = ?

A heat engine takes in 2900 kJ of heat from a hot reservoir and rejects 1740 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2900 kJQL = 1740 kJ
W = kJ
3.Medium
TH​ = 675 °CTL​ = 40 °CEQH​ = 3400 kJQL​W = ?

A heat engine works between a hot reservoir at 675 °C and a cold reservoir at 40 °C. It takes in 3400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 675 °CTL = 40 °CQH = 3400 kJ
Wmax = kJ
4.Medium
TH​ = 35 °CTL​ = 2 °CRQ̇H​ = ?Q̇L​ = 3.5 kWẆ

A reversible refrigerator keeps a cold room at 2 °C by removing 3.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = 2 °CTH = 35 °CQ̇L = 3.5 kW
Q̇H = kW
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 18 kWQ̇L​Ẇ = ?

A heat pump delivers 18 kW of heat to a heating system at 22 °C, taking heat from a source at 7 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 7 °CηII = 45%Q̇H = 18 kW
Ẇ = kW
6.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 14 kW
Ẇmin = kW

Answer key

  1. 1. W = 1175 kJ
  2. 2. W = 1160 kJ
  3. 3. Wmax = 2277 kJ
  4. 4. Q̇H = 3.92 kW
  5. 5. Ẇ = 2.033 kW
  6. 6. Ẇmin = 0.9487 kW

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