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​ = 4100 kJQL​ = 2460 kJW = ?

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 2460 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4100 kJQL = 2460 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.3 delivers 10 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.3Q̇H = 10 kW
Ẇ = kW
3.Medium
TH​ = 800 °CTL​ = 40 °CEQH​ = 2500 kJQL​W = ?

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 40 °C. It takes in 2500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 800 °CTL = 40 °CQH = 2500 kJ
Wmax = kJ
4.Medium
TH​ = 325 °CTL​ = ?EQH​ = 4400 kJQL​ = 2414 kJW

A reversible (Carnot) heat engine takes in 4400 kJ of heat from a reservoir at 325 °C and rejects 2414 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 325 °CQH = 4400 kJQL = 2414 kJ
TL = °C
5.Hard
TH​ = 20 °CTL​ = -5 °CHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -5 °C outside, delivering 7 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -5 °CQ̇H = 7 kW
Ẇmin = kW
6.Hard
TH​ = 35 °CTL​ = 5 °CHPQ̇H​ = 5.5 kWQ̇L​Ẇ = ?

A heat pump delivers 5.5 kW of heat to a heating system at 35 °C, taking heat from a source at 5 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 35 °CTL = 5 °CηII = 60%Q̇H = 5.5 kW
Ẇ = kW

Answer key

  1. 1. W = 1640 kJ
  2. 2. Ẇ = 3.03 kW
  3. 3. Wmax = 1770 kJ
  4. 4. TL = 55.02 °C
  5. 5. Ẇmin = 0.597 kW
  6. 6. Ẇ = 0.8924 kW

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