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
houseoutside airHPQ̇H​ = 18 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.1 delivers 18 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.1Q̇H = 18 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 1800 kJQL​ = 1170 kJW = ?

A heat engine takes in 1800 kJ of heat from a hot reservoir and rejects 1170 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1800 kJQL = 1170 kJ
W = kJ
3.Medium
TH​ = 375 °CTL​ = 20 °CEQH​ = 2400 kJQL​W = ?

A heat engine works between a hot reservoir at 375 °C and a cold reservoir at 20 °C. It takes in 2400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 375 °CTL = 20 °CQH = 2400 kJ
Wmax = kJ
4.Medium
TH​ = 675 °CTL​ = 40 °CEQH​ = 3600 kJQL​W = ?

A heat engine works between a hot reservoir at 675 °C and a cold reservoir at 40 °C. It takes in 3600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 675 °CTL = 40 °CQH = 3600 kJ
Wmax = kJ
5.Hard
TH​ = 21 °CTL​ = 0 °CHPQ̇H​ = 19 kWQ̇L​Ẇ = ?

A heat pump delivers 19 kW of heat to a heating system at 21 °C, taking heat from a source at 0 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = 0 °CηII = 30%Q̇H = 19 kW
Ẇ = kW
6.Hard
TH​ = 700 °CT0​ = 27 °CTL​ = -5 °CERWQ̇H​ = 70 kWQ̇L​ = ?

A Carnot heat engine receives 70 kW of heat from a source at 700 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -5 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 700 °CT0 = 27 °CTL = -5 °CQ̇H = 70 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 4.39 kW
  2. 2. W = 630 kJ
  3. 3. Wmax = 1315 kJ
  4. 4. Wmax = 2411 kJ
  5. 5. Ẇ = 4.522 kW
  6. 6. Q̇L = 405.7 kW

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