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​ = 2500 kJQL​ = 1750 kJW

A heat engine takes in 2500 kJ of heat from a hot reservoir and rejects 1750 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2500 kJQL = 1750 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 0.5 kWẆ = 0.2 kW

A refrigerator removes heat from its cold space at a rate of 0.5 kW while its compressor uses 0.2 kW of power. Find its coefficient of performance COPR.

Q̇L = 0.5 kWẆ = 0.2 kW
COPR =
3.Medium
TH​ = 500 °CTL​ = 30 °CEQH​ = 3200 kJQL​W = ?

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 30 °C. It takes in 3200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 500 °CTL = 30 °CQH = 3200 kJ
Wmax = kJ
4.Medium
TH​ = 250 °CTL​ = 30 °CEQH​ = 4700 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 30 °C. It takes in 4700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 30 °CQH = 4700 kJ
Wmax = kJ
5.Hard
TH​ = 30 °CTL​ = -10 °CRQ̇H​Q̇L​ = 1 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 30 °C, removing heat from the cold space at 1 kW. Find the highest possible coefficient of performance COPmax.

TH = 30 °CTL = -10 °CQ̇L = 1 kW
COPmax =
6.Hard
TH​ = 850 °CTL​ = 25 °CEQH​ = 2000 kJQL​ = 1120 kJW = 880 kJ

A heat engine takes in 2000 kJ of heat from a reservoir at 850 °C, produces 880 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 850 °CTL = 25 °CQH = 2000 kJW = 880 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 30 %
  2. 2. COPR = 2.5
  3. 3. Wmax = 1945 kJ
  4. 4. Wmax = 1976 kJ
  5. 5. COPmax = 6.579
  6. 6. Sgen = 1.976 kJ/K

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