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 its thermal efficiency η.

QH = 4800 kJQL = 3840 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 12.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.8 delivers 12.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.8Q̇H = 12.5 kW
Ẇ = kW
3.Medium
TH​ = 375 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 375 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 575 °CTL​ = 10 °CEQH​ = 800 kJQL​W = ?

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 10 °C. It takes in 800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 575 °CTL = 10 °CQH = 800 kJ
Wmax = kJ
5.Hard
TH​ = 800 °CTL​ = 30 °CEQH​ = 1200 kJQL​ = 600 kJW = 600 kJ

A heat engine takes in 1200 kJ of heat from a reservoir at 800 °C, produces 600 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 800 °CTL = 30 °CQH = 1200 kJW = 600 kJ
Sgen = kJ/K
6.Hard
TH​ = 450 °CTL​ = 40 °CEQH​ = 2000 kJQL​ = 1320 kJW = 680 kJ

A heat engine takes in 2000 kJ of heat from a reservoir at 450 °C, produces 680 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 450 °CTL = 40 °CQH = 2000 kJW = 680 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 20 %
  2. 2. Ẇ = 3.289 kW
  3. 3. ηmax = 57.09 %
  4. 4. Wmax = 532.9 kJ
  5. 5. Sgen = 0.861 kJ/K
  6. 6. Sgen = 1.45 kJ/K

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