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​ = 14 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.7 delivers 14 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.7Q̇H = 14 kW
Ẇ = kW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 50%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 100 MWη = 50%
Q̇L = MW
3.Medium
TH​ = 275 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 275 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 35 °CTL​ = -10 °CRQ̇H​ = ?Q̇L​ = 0.5 kWẆ

A reversible refrigerator keeps a cold room at -10 °C by removing 0.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = -10 °CTH = 35 °CQ̇L = 0.5 kW
Q̇H = kW
5.Hard
TH​ = 32 °CTL​ = -20 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -20 °C in a kitchen at 32 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -20 °CQ̇L = 1.5 kW
Ẇmin = kW
6.Hard
TH​ = 950 °CT0​ = 30 °CTL​ = -10 °CERWQ̇H​ = 140 kWQ̇L​ = ?

A Carnot heat engine receives 140 kW of heat from a source at 950 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -10 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 950 °CT0 = 30 °CTL = -10 °CQ̇H = 140 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 3.784 kW
  2. 2. Q̇L = 100 MW
  3. 3. ηmax = 42.87 %
  4. 4. Q̇H = 0.5855 kW
  5. 5. Ẇmin = 0.3081 kW
  6. 6. Q̇L = 692.8 kW

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