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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 30%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 3900 kJQL​ = 2340 kJW

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2340 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3900 kJQL = 2340 kJ
η = %
3.Medium
TH​ = 500 °CTL​ = ?EQH​ = 4500 kJQL​ = 1881 kJW

A reversible (Carnot) heat engine takes in 4500 kJ of heat from a reservoir at 500 °C and rejects 1881 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 500 °CQH = 4500 kJQL = 1881 kJ
TL = °C
4.Medium
TH​ = 800 °CTL​ = 35 °CEQH​QL​η = 39%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 39%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 35 °Cη = 39%
ηII = %
5.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump delivers 12 kW of heat to a heating system at 20 °C, taking heat from a source at 0 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = 0 °CηII = 45%Q̇H = 12 kW
Ẇ = kW
6.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 12 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 7 °CQ̇H = 12 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 2000 MW
  2. 2. η = 40 %
  3. 3. TL = 50.03 °C
  4. 4. ηII = 54.71 %
  5. 5. Ẇ = 1.819 kW
  6. 6. Ẇmin = 0.5322 kW

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