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​ = 1800 kJQL​ = 1440 kJW = ?

A heat engine takes in 1800 kJ of heat from a hot reservoir and rejects 1440 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1800 kJQL = 1440 kJ
W = kJ
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 0.84 kWẆ = 0.3 kW

A refrigerator removes heat from its cold space at a rate of 0.84 kW while its compressor uses 0.3 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 0.84 kWẆ = 0.3 kW
Q̇H = kW
3.Medium
TH​ = 30 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 5 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 5 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = -10 °CTH = 30 °CQ̇L = 5 kW
Q̇H = kW
4.Medium
TH​ = 400 °CTL​ = ?EQH​ = 3900 kJQL​ = 1669 kJW

A reversible (Carnot) heat engine takes in 3900 kJ of heat from a reservoir at 400 °C and rejects 1669 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 400 °CQH = 3900 kJQL = 1669 kJ
TL = °C
5.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 12 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 12 kW
Ẇmin = kW
6.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 9 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 9 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = 0 °CQ̇H = 9 kW
COPmax =

Answer key

  1. 1. W = 360 kJ
  2. 2. Q̇H = 1.14 kW
  3. 3. Q̇H = 5.76 kW
  4. 4. TL = 14.92 °C
  5. 5. Ẇmin = 0.8131 kW
  6. 6. COPmax = 14.66

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