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​ = 2600 kJQL​ = 1820 kJW

A heat engine takes in 2600 kJ of heat from a hot reservoir and rejects 1820 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2600 kJQL = 1820 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 55%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 150 MWη = 55%
Q̇L = MW
3.Medium
TH​ = 275 °CTL​ = ?EQH​ = 3200 kJQL​ = 1624 kJW

A reversible (Carnot) heat engine takes in 3200 kJ of heat from a reservoir at 275 °C and rejects 1624 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 275 °CQH = 3200 kJQL = 1624 kJ
TL = °C
4.Medium
TH​ = 225 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 225 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 225 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 20 °CTL​ = -5 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -5 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -5 °CQ̇H = 13 kW
Ẇmin = kW
6.Hard
TH​ = 45 °CTL​ = 7 °CHPQ̇H​ = 16 kWQ̇L​Ẇ = ?

A heat pump delivers 16 kW of heat to a heating system at 45 °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 = 45 °CTL = 7 °CηII = 45%Q̇H = 16 kW
Ẇ = kW

Answer key

  1. 1. η = 30 %
  2. 2. Q̇L = 122.7 MW
  3. 3. TL = 5.036 °C
  4. 4. ηmax = 44.16 %
  5. 5. Ẇmin = 1.109 kW
  6. 6. Ẇ = 4.247 kW

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