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​ = 17.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3 delivers 17.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3Q̇H = 17.5 kW
Ẇ = kW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 25%
Q̇L = MW
3.Medium
TH​ = 400 °CTL​ = 35 °CEQH​ = 3000 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 35 °C. It takes in 3000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 35 °CQH = 3000 kJ
Wmax = kJ
4.Medium
TH​ = 600 °CTL​ = 25 °CEQH​ = 1400 kJQL​W = ?

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 25 °C. It takes in 1400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 600 °CTL = 25 °CQH = 1400 kJ
Wmax = kJ
5.Hard
TH​ = 25 °CTL​ = 2 °CRQ̇H​Q̇L​ = 4 kWẆ

A refrigerator keeps its cold space at 2 °C in a kitchen at 25 °C, removing heat from the cold space at 4 kW. Find the highest possible coefficient of performance COPmax.

TH = 25 °CTL = 2 °CQ̇L = 4 kW
COPmax =
6.Hard
TH​ = 20 °CTL​ = -5 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is -5 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = -5 °CQ̇H = 13 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 5.833 kW
  2. 2. Q̇L = 600 MW
  3. 3. Wmax = 1627 kJ
  4. 4. Wmax = 921.9 kJ
  5. 5. COPmax = 11.96
  6. 6. Ẇmin = 1.109 kW

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