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​ = 4800 kJQL​ = 3840 kJW = ?

A heat engine takes in 4800 kJ of heat from a hot reservoir and rejects 3840 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4800 kJQL = 3840 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 7.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.3 delivers 7.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.3Q̇H = 7.5 kW
Q̇L = kW
3.Medium
TH​ = 525 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 525 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 525 °CTL = 25 °C
ηmax = %
4.Medium
TH​ = 350 °CTL​ = 35 °CEQH​QL​η = 33%

A heat engine receives heat from a source at 350 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 33%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 350 °CTL = 35 °Cη = 33%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 0 °CHPQ̇H​ = 5 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 0 °C outside, delivering 5 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 0 °CQ̇H = 5 kW
COPmax =
6.Hard
TH​ = 30 °CTL​ = 2 °CRQ̇H​Q̇L​ = 2.5 kWẆ = ?

A refrigerator keeps its cold space at 2 °C in a kitchen at 30 °C, removing heat from the cold space at 2.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 2 °CQ̇L = 2.5 kW
Ẇmin = kW

Answer key

  1. 1. W = 960 kJ
  2. 2. Q̇L = 5.756 kW
  3. 3. ηmax = 62.64 %
  4. 4. ηII = 65.28 %
  5. 5. COPmax = 14.01
  6. 6. Ẇmin = 0.2544 kW

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