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​ = 4500 kJQL​ = 2925 kJW = ?

A heat engine takes in 4500 kJ of heat from a hot reservoir and rejects 2925 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4500 kJQL = 2925 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.3 delivers 19.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.3Q̇H = 19.5 kW
Ẇ = kW
3.Medium
TH​ = 700 °CTL​ = 25 °CEQH​ = 4400 kJQL​W = ?

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 25 °C. It takes in 4400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 700 °CTL = 25 °CQH = 4400 kJ
Wmax = kJ
4.Medium
TH​ = 525 °CTL​ = 40 °CEQH​ = 1100 kJQL​W = ?

A heat engine works between a hot reservoir at 525 °C and a cold reservoir at 40 °C. It takes in 1100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 525 °CTL = 40 °CQH = 1100 kJ
Wmax = kJ
5.Hard
TH​ = 55 °CTL​ = 10 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump delivers 10 kW of heat to a heating system at 55 °C, taking heat from a source at 10 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 10 °CηII = 30%Q̇H = 10 kW
Ẇ = kW
6.Hard
TH​ = 35 °CTL​ = -20 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 35 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = -20 °CQ̇L = 1.5 kW
Ẇmin = kW

Answer key

  1. 1. W = 1575 kJ
  2. 2. Ẇ = 5.909 kW
  3. 3. Wmax = 3052 kJ
  4. 4. Wmax = 668.4 kJ
  5. 5. Ẇ = 4.571 kW
  6. 6. Ẇmin = 0.3259 kW

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