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​ = 3400 kJQL​ = 1870 kJW

A heat engine takes in 3400 kJ of heat from a hot reservoir and rejects 1870 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3400 kJQL = 1870 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 4500 kJQL​ = 2475 kJW = ?

A heat engine takes in 4500 kJ of heat from a hot reservoir and rejects 2475 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4500 kJQL = 2475 kJ
W = kJ
3.Medium
TH​ = 300 °CTL​ = 30 °CEQH​QL​η = 26%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 26%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 30 °Cη = 26%
ηII = %
4.Medium
TH​ = 800 °CTL​ = 15 °CEQH​QL​η = 44%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 44%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 15 °Cη = 44%
ηII = %
5.Hard
700 °CTm​ = ?10 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 700 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 10 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 700 °CTL = 10 °C
Tm = °C
6.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 15 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 2 °CQ̇H = 15 kW
Ẇmin = kW

Answer key

  1. 1. η = 45 %
  2. 2. W = 2025 kJ
  3. 3. ηII = 55.19 %
  4. 4. ηII = 60.15 %
  5. 5. Tm = 251.8 °C
  6. 6. Ẇmin = 0.9689 kW

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