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
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 400 MW

A power plant delivers a net power output of 400 MW with a thermal efficiency of 38%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 400 MWη = 38%
Q̇L = MW
2.Easy
houseoutside airHPQ̇H​ = 11.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.3 delivers 11.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.3Q̇H = 11.5 kW
Ẇ = kW
3.Medium
TH​ = 35 °CTL​ = -30 °CRQ̇H​ = ?Q̇L​ = 4.5 kWẆ

A reversible refrigerator keeps a cold room at -30 °C by removing 4.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -30 °CTH = 35 °CQ̇L = 4.5 kW
Q̇H = kW
4.Medium
TH​ = 400 °CTL​ = 35 °CEQH​ = 4000 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 35 °C. It takes in 4000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 35 °CQH = 4000 kJ
Wmax = kJ
5.Hard
TH​ = 550 °CT0​ = 27 °CTL​ = 0 °CERWQ̇H​ = 110 kWQ̇L​ = ?

A Carnot heat engine receives 110 kW of heat from a source at 550 °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 0 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 550 °CT0 = 27 °CTL = 0 °CQ̇H = 110 kW
Q̇L = kW
6.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 18.5 kWQ̇L​Ẇ = ?

A heat pump delivers 18.5 kW of heat to a heating system at 21 °C, taking heat from a source at 5 °C. Its actual COP is 45% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 21 °CTL = 5 °CηII = 45%Q̇H = 18.5 kW
Ẇ = kW

Answer key

  1. 1. Q̇L = 652.6 MW
  2. 2. Ẇ = 2.674 kW
  3. 3. Q̇H = 5.703 kW
  4. 4. Wmax = 2169 kJ
  5. 5. Q̇L = 707.1 kW
  6. 6. Ẇ = 2.236 kW

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