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​ = 1980 kJW = ?

A heat engine takes in 3600 kJ of heat from a hot reservoir and rejects 1980 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3600 kJQL = 1980 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4300 kJQL​ = 3225 kJW = ?

A heat engine takes in 4300 kJ of heat from a hot reservoir and rejects 3225 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4300 kJQL = 3225 kJ
W = kJ
3.Medium
TH​ = 400 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 400 °CTL = 25 °C
ηmax = %
4.Medium
TH​ = 30 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 3 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 3 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 30 °CQ̇L = 3 kW
Q̇H = kW
5.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 18 kWQ̇L​Ẇ = ?

A heat pump delivers 18 kW of heat to a heating system at 21 °C, taking heat from a source at -5 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = -5 °CηII = 35%Q̇H = 18 kW
Ẇ = kW
6.Hard
TH​ = 55 °CTL​ = 0 °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 0 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 0 °CηII = 55%Q̇H = 9 kW
Ẇ = kW

Answer key

  1. 1. W = 1620 kJ
  2. 2. W = 1075 kJ
  3. 3. ηmax = 55.71 %
  4. 4. Q̇H = 3.564 kW
  5. 5. Ẇ = 4.546 kW
  6. 6. Ẇ = 2.743 kW

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