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​ = 4400 kJQL​ = 2640 kJW

A heat engine takes in 4400 kJ of heat from a hot reservoir and rejects 2640 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4400 kJQL = 2640 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 1200 kJQL​ = 780 kJW

A heat engine takes in 1200 kJ of heat from a hot reservoir and rejects 780 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1200 kJQL = 780 kJ
η = %
3.Medium
TH​ = 700 °CTL​ = 10 °CEQH​QL​η = 46%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 46%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 10 °Cη = 46%
ηII = %
4.Medium
TH​ = 900 °CTL​ = 25 °CEQH​QL​η = 56%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 56%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 25 °Cη = 56%
ηII = %
5.Hard
1050 °CTm​ = ?25 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 1050 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 25 °C. Both engines produce the same work. Find Tm in °C.

TH = 1050 °CTL = 25 °C
Tm = °C
6.Hard
850 °CTm​ = ?35 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 850 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 35 °C. Both engines produce the same work. Find Tm in °C.

TH = 850 °CTL = 35 °C
Tm = °C

Answer key

  1. 1. η = 40 %
  2. 2. η = 35 %
  3. 3. ηII = 64.88 %
  4. 4. ηII = 75.08 %
  5. 5. Tm = 537.5 °C
  6. 6. Tm = 442.5 °C

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