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​ = 4000 kJQL​ = 2200 kJW

A heat engine takes in 4000 kJ of heat from a hot reservoir and rejects 2200 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4000 kJQL = 2200 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 2800 kJQL​ = 1960 kJW = ?

A heat engine takes in 2800 kJ of heat from a hot reservoir and rejects 1960 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2800 kJQL = 1960 kJ
W = kJ
3.Medium
TH​ = 650 °CTL​ = 20 °CEQH​QL​η = 44%

A heat engine receives heat from a source at 650 °C and rejects heat to the surroundings at 20 °C. Its actual thermal efficiency is 44%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 650 °CTL = 20 °Cη = 44%
ηII = %
4.Medium
TH​ = 250 °CTL​ = 30 °CEQH​ = 3900 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 30 °C. It takes in 3900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 30 °CQH = 3900 kJ
Wmax = kJ
5.Hard
TH​ = 28 °CTL​ = -18 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at -18 °C in a kitchen at 28 °C, removing heat from the cold space at 2.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = -18 °CQ̇L = 2.5 kW
COPmax =
6.Hard
TH​ = 30 °CTL​ = 2 °CRQ̇H​Q̇L​ = 5 kWẆ = ?

A refrigerator keeps its cold space at 2 °C in a kitchen at 30 °C, removing heat from the cold space at 5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 2 °CQ̇L = 5 kW
Ẇmin = kW

Answer key

  1. 1. η = 45 %
  2. 2. W = 840 kJ
  3. 3. ηII = 64.47 %
  4. 4. Wmax = 1640 kJ
  5. 5. COPmax = 5.547
  6. 6. Ẇmin = 0.5088 kW

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