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​ = 6.8 kWẆ = 1.7 kW

A refrigerator removes heat from its cold space at a rate of 6.8 kW while its compressor uses 1.7 kW of power. Find its coefficient of performance COPR.

Q̇L = 6.8 kWẆ = 1.7 kW
COPR =
2.Easy
hot reservoircold reservoirEQH​ = 4600 kJQL​ = 3450 kJW

A heat engine takes in 4600 kJ of heat from a hot reservoir and rejects 3450 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4600 kJQL = 3450 kJ
η = %
3.Medium
TH​ = 375 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 375 °CTL = 10 °C
ηmax = %
4.Medium
TH​ = 40 °CTL​ = -18 °CRQ̇H​ = ?Q̇L​ = 4 kWẆ

A reversible refrigerator keeps a cold room at -18 °C by removing 4 kW of heat, and rejects heat to the surroundings at 40 °C. Find the rate Q̇H at which it rejects heat.

TL = -18 °CTH = 40 °CQ̇L = 4 kW
Q̇H = kW
5.Hard
TH​ = 550 °CTL​ = 25 °CEQH​ = 500 kJQL​ = 245 kJW = 255 kJ

A heat engine takes in 500 kJ of heat from a reservoir at 550 °C, produces 255 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 550 °CTL = 25 °CQH = 500 kJW = 255 kJ
Sgen = kJ/K
6.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 19 kWQ̇L​Ẇ = ?

A heat pump delivers 19 kW of heat to a heating system at 20 °C, taking heat from a source at -10 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = -10 °CηII = 55%Q̇H = 19 kW
Ẇ = kW

Answer key

  1. 1. COPR = 4
  2. 2. η = 25 %
  3. 3. ηmax = 56.31 %
  4. 4. Q̇H = 4.909 kW
  5. 5. Sgen = 0.2143 kJ/K
  6. 6. Ẇ = 3.535 kW

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