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 42%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 600 MWη = 42%
Q̇H = MW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 38%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 38%
Q̇L = MW
3.Medium
TH​ = 425 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 425 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 425 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 650 °CTL​ = 10 °CEQH​QL​η = 52%

A heat engine receives heat from a source at 650 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 52%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 650 °CTL = 10 °Cη = 52%
ηII = %
5.Hard
650 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 650 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 40 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 650 °CTL = 40 °C
Tm = °C
6.Hard
TH​ = 20 °CTL​ = 7 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 7 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 7 °CQ̇H = 6 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 1429 MW
  2. 2. Q̇L = 81.58 MW
  3. 3. ηmax = 55.15 %
  4. 4. ηII = 75.01 %
  5. 5. Tm = 264.5 °C
  6. 6. Ẇmin = 0.2661 kW

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