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
kitchencold spaceRQ̇H​Q̇L​ = 6.25 kWẆ = 2.5 kW

A refrigerator removes heat from its cold space at a rate of 6.25 kW while its compressor uses 2.5 kW of power. Find its coefficient of performance COPR.

Q̇L = 6.25 kWẆ = 2.5 kW
COPR =
2.Easy
houseoutside airHPQ̇H​ = 8 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.4 delivers 8 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.4Q̇H = 8 kW
Q̇L = kW
3.Medium
TH​ = 400 °CTL​ = 35 °CEQH​ = 3800 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 35 °C. It takes in 3800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 35 °CQH = 3800 kJ
Wmax = kJ
4.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 = %
5.Hard
TH​ = 750 °CTL​ = 40 °CEQH​ = 1400 kJQL​ = 616 kJW = 784 kJ

A heat engine takes in 1400 kJ of heat from a reservoir at 750 °C, produces 784 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 40 °CQH = 1400 kJW = 784 kJ
Sgen = kJ/K
6.Hard
TH​ = 55 °CTL​ = -10 °CHPQ̇H​ = 16.5 kWQ̇L​Ẇ = ?

A heat pump delivers 16.5 kW of heat to a heating system at 55 °C, taking heat from a source at -10 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = -10 °CηII = 50%Q̇H = 16.5 kW
Ẇ = kW

Answer key

  1. 1. COPR = 2.5
  2. 2. Q̇L = 5.647 kW
  3. 3. Wmax = 2060 kJ
  4. 4. ηmax = 62.64 %
  5. 5. Sgen = 0.5988 kJ/K
  6. 6. Ẇ = 6.537 kW

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