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​ = 3280 kJW

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 3280 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4100 kJQL = 3280 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 2400 kJQL​ = 1920 kJW = ?

A heat engine takes in 2400 kJ of heat from a hot reservoir and rejects 1920 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2400 kJQL = 1920 kJ
W = kJ
3.Medium
TH​ = 900 °CTL​ = 35 °CEQH​QL​η = 29%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 29%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 35 °Cη = 29%
ηII = %
4.Medium
TH​ = 325 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 40 °C
ηmax = %
5.Hard
TH​ = 650 °CT0​ = 30 °CTL​ = 0 °CERWQ̇H​ = 100 kWQ̇L​ = ?

A Carnot heat engine receives 100 kW of heat from a source at 650 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at 0 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 30 °CTL = 0 °CQ̇H = 100 kW
Q̇L = kW
6.Hard
TH​ = 28 °CTL​ = 2 °CRQ̇H​Q̇L​ = 4 kWẆ

A refrigerator keeps its cold space at 2 °C in a kitchen at 28 °C, removing heat from the cold space at 4 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = 2 °CQ̇L = 4 kW
COPmax =

Answer key

  1. 1. η = 20 %
  2. 2. W = 480 kJ
  3. 3. ηII = 39.33 %
  4. 4. ηmax = 47.65 %
  5. 5. Q̇L = 611.5 kW
  6. 6. COPmax = 10.58

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