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 = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 35%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 35%
Q̇H = MW
2.Easy
houseoutside airHPQ̇H​ = 12.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3 delivers 12.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3Q̇H = 12.5 kW
Ẇ = kW
3.Medium
TH​ = 625 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 625 °CTL = 10 °C
ηmax = %
4.Medium
TH​ = 575 °CTL​ = 40 °CEQH​ = 2900 kJQL​W = ?

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 40 °C. It takes in 2900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 575 °CTL = 40 °CQH = 2900 kJ
Wmax = kJ
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 7 °CQ̇H = 10 kW
Ẇmin = kW
6.Hard
TH​ = 20 °CTL​ = 5 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 5 °C outside, delivering 8 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 5 °CQ̇H = 8 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 571.4 MW
  2. 2. Ẇ = 4.167 kW
  3. 3. ηmax = 68.47 %
  4. 4. Wmax = 1829 kJ
  5. 5. Ẇmin = 0.5082 kW
  6. 6. Ẇmin = 0.4093 kW

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