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​ = 2900 kJQL​ = 1595 kJW = ?

A heat engine takes in 2900 kJ of heat from a hot reservoir and rejects 1595 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2900 kJQL = 1595 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 3200 kJQL​ = 2400 kJW

A heat engine takes in 3200 kJ of heat from a hot reservoir and rejects 2400 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3200 kJQL = 2400 kJ
η = %
3.Medium
TH​ = 425 °CTL​ = ?EQH​ = 2300 kJQL​ = 949 kJW

A reversible (Carnot) heat engine takes in 2300 kJ of heat from a reservoir at 425 °C and rejects 949 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 425 °CQH = 2300 kJQL = 949 kJ
TL = °C
4.Medium
TH​ = 300 °CTL​ = 35 °CEQH​QL​η = 28%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 28%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 35 °Cη = 28%
ηII = %
5.Hard
800 °CTm​ = ?25 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 800 °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 have the same thermal efficiency. Find Tm in °C.

TH = 800 °CTL = 25 °C
Tm = °C
6.Hard
TH​ = 450 °CTL​ = 20 °CEQH​ = 4900 kJQL​ = 2548 kJW = 2352 kJ

A heat engine takes in 4900 kJ of heat from a reservoir at 450 °C, produces 2352 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 450 °CTL = 20 °CQH = 4900 kJW = 2352 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 1305 kJ
  2. 2. η = 25 %
  3. 3. TL = 14.91 °C
  4. 4. ηII = 60.56 %
  5. 5. Tm = 292.5 °C
  6. 6. Sgen = 1.916 kJ/K

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