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 = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 50 MWη = 30%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 1300 kJQL​ = 715 kJW

A heat engine takes in 1300 kJ of heat from a hot reservoir and rejects 715 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1300 kJQL = 715 kJ
η = %
3.Medium
TH​ = 850 °CTL​ = 25 °CEQH​QL​η = 37%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 37%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 25 °Cη = 37%
ηII = %
4.Medium
TH​ = 275 °CTL​ = ?EQH​ = 1100 kJQL​ = 578 kJW

A reversible (Carnot) heat engine takes in 1100 kJ of heat from a reservoir at 275 °C and rejects 578 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 275 °CQH = 1100 kJQL = 578 kJ
TL = °C
5.Hard
TH​ = 21 °CTL​ = 0 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 0 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 0 °CQ̇H = 8 kW
Ẇmin = kW
6.Hard
1200 °CTm​ = ?15 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 1200 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 15 °C. Both engines produce the same work. Find Tm in °C.

TH = 1200 °CTL = 15 °C
Tm = °C

Answer key

  1. 1. Q̇H = 166.7 MW
  2. 2. η = 45 %
  3. 3. ηII = 50.37 %
  4. 4. TL = 14.88 °C
  5. 5. Ẇmin = 0.5711 kW
  6. 6. Tm = 607.5 °C

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