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​ = 4100 kJQL​ = 2255 kJW

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 2255 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4100 kJQL = 2255 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 600 kJQL​ = 330 kJW

A heat engine takes in 600 kJ of heat from a hot reservoir and rejects 330 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 600 kJQL = 330 kJ
η = %
3.Medium
TH​ = 625 °CTL​ = ?EQH​ = 1900 kJQL​ = 694 kJW

A reversible (Carnot) heat engine takes in 1900 kJ of heat from a reservoir at 625 °C and rejects 694 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 625 °CQH = 1900 kJQL = 694 kJ
TL = °C
4.Medium
TH​ = 300 °CTL​ = 10 °CEQH​QL​η = 25%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 25%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 10 °Cη = 25%
ηII = %
5.Hard
TH​ = 900 °CTL​ = 10 °CEQH​ = 4900 kJQL​ = 1911 kJW = 2989 kJ

A heat engine takes in 4900 kJ of heat from a reservoir at 900 °C, produces 2989 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 900 °CTL = 10 °CQH = 4900 kJW = 2989 kJ
Sgen = kJ/K
6.Hard
950 °CTm​ = ?25 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 950 °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 = 950 °CTL = 25 °C
Tm = °C

Answer key

  1. 1. η = 45 %
  2. 2. η = 45 %
  3. 3. TL = 54.91 °C
  4. 4. ηII = 49.41 %
  5. 5. Sgen = 2.572 kJ/K
  6. 6. Tm = 487.5 °C

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