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​ = 4600 kJQL​ = 2990 kJW = ?

A heat engine takes in 4600 kJ of heat from a hot reservoir and rejects 2990 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4600 kJQL = 2990 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3 delivers 19.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3Q̇H = 19.5 kW
Ẇ = kW
3.Medium
TH​ = 650 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 650 °CTL = 25 °C
ηmax = %
4.Medium
TH​ = 375 °CTL​ = 30 °CEQH​ = 1500 kJQL​W = ?

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 30 °C. It takes in 1500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 375 °CTL = 30 °CQH = 1500 kJ
Wmax = kJ
5.Hard
TH​ = 30 °CTL​ = 4 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 30 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 4 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 22 °CTL​ = 5 °CHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump delivers 19.5 kW of heat to a heating system at 22 °C, taking heat from a source at 5 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 5 °CηII = 50%Q̇H = 19.5 kW
Ẇ = kW

Answer key

  1. 1. W = 1610 kJ
  2. 2. Ẇ = 6.5 kW
  3. 3. ηmax = 67.7 %
  4. 4. Wmax = 798.4 kJ
  5. 5. Ẇmin = 0.1876 kW
  6. 6. Ẇ = 2.246 kW

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