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​ = 3000 kJQL​ = 1800 kJW

A heat engine takes in 3000 kJ of heat from a hot reservoir and rejects 1800 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3000 kJQL = 1800 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 3.38 kWẆ = 1.3 kW

A refrigerator removes heat from its cold space at a rate of 3.38 kW while its compressor uses 1.3 kW of power. Find its coefficient of performance COPR.

Q̇L = 3.38 kWẆ = 1.3 kW
COPR =
3.Medium
TH​ = 775 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 775 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 775 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 725 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 725 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 725 °CTL = 25 °C
ηmax = %
5.Hard
TH​ = 600 °CT0​ = 20 °CTL​ = -20 °CERWQ̇H​ = 130 kWQ̇L​ = ?

A Carnot heat engine receives 130 kW of heat from a source at 600 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -20 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 600 °CT0 = 20 °CTL = -20 °CQ̇H = 130 kW
Q̇L = kW
6.Hard
TH​ = 35 °CTL​ = -18 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at -18 °C in a kitchen at 35 °C, removing heat from the cold space at 2.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 35 °CTL = -18 °CQ̇L = 2.5 kW
COPmax =

Answer key

  1. 1. η = 40 %
  2. 2. COPR = 2.6
  3. 3. ηmax = 71.08 %
  4. 4. ηmax = 70.13 %
  5. 5. Q̇L = 546.5 kW
  6. 6. COPmax = 4.814

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