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​ = 4700 kJQL​ = 3290 kJW = ?

A heat engine takes in 4700 kJ of heat from a hot reservoir and rejects 3290 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4700 kJQL = 3290 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4800 kJQL​ = 3600 kJW = ?

A heat engine takes in 4800 kJ of heat from a hot reservoir and rejects 3600 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4800 kJQL = 3600 kJ
W = kJ
3.Medium
TH​ = 325 °CTL​ = ?EQH​ = 2300 kJQL​ = 1185 kJW

A reversible (Carnot) heat engine takes in 2300 kJ of heat from a reservoir at 325 °C and rejects 1185 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 325 °CQH = 2300 kJQL = 1185 kJ
TL = °C
4.Medium
TH​ = 750 °CTL​ = 25 °CEQH​QL​η = 50%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 50%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 25 °Cη = 50%
ηII = %
5.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 have the same thermal efficiency. Find Tm in °C.

TH = 950 °CTL = 25 °C
Tm = °C
6.Hard
TH​ = 32 °CTL​ = 4 °CRQ̇H​Q̇L​ = 4.5 kWẆ

A refrigerator keeps its cold space at 4 °C in a kitchen at 32 °C, removing heat from the cold space at 4.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = 4 °CQ̇L = 4.5 kW
COPmax =

Answer key

  1. 1. W = 1410 kJ
  2. 2. W = 1200 kJ
  3. 3. TL = 35.03 °C
  4. 4. ηII = 70.56 %
  5. 5. Tm = 330.7 °C
  6. 6. COPmax = 9.898

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