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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Name: ____________________   Date: ____________

1.Easy
houseoutside airHPQ̇H​ = 8.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.9 delivers 8.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.9Q̇H = 8.5 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 17.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.1 delivers 17.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.1Q̇H = 17.5 kW
Q̇L = kW
3.Medium
TH​ = 650 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 650 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 750 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 750 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 750 °CTL = 25 °C
ηmax = %
5.Hard
900 °CTm​ = ?30 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 900 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 30 °C. Both engines produce the same work. Find Tm in °C.

TH = 900 °CTL = 30 °C
Tm = °C
6.Hard
TH​ = 650 °CT0​ = 30 °CTL​ = -25 °CERWQ̇H​ = 150 kWQ̇L​ = ?

A Carnot heat engine receives 150 kW of heat from a source at 650 °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 -25 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 30 °CTL = -25 °CQ̇H = 150 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 1.735 kW
  2. 2. Q̇L = 13.23 kW
  3. 3. ηmax = 67.16 %
  4. 4. ηmax = 70.86 %
  5. 5. Tm = 465 °C
  6. 6. Q̇L = 454.5 kW

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