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​ = 11 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.3 delivers 11 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.3Q̇H = 11 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 4.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.1 delivers 4.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.1Q̇H = 4.5 kW
Ẇ = kW
3.Medium
TH​ = 575 °CTL​ = 40 °CEQH​ = 4800 kJQL​W = ?

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 40 °C. It takes in 4800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 575 °CTL = 40 °CQH = 4800 kJ
Wmax = kJ
4.Medium
TH​ = 500 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 500 °CTL = 10 °C
ηmax = %
5.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 6 kW
Ẇmin = kW
6.Hard
950 °CTm​ = ?25 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 950 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 25 °C. Both engines produce the same work. Find Tm in °C.

TH = 950 °CTL = 25 °C
Tm = °C

Answer key

  1. 1. Ẇ = 2.558 kW
  2. 2. Ẇ = 1.098 kW
  3. 3. Wmax = 3028 kJ
  4. 4. ηmax = 63.38 %
  5. 5. Ẇmin = 0.4066 kW
  6. 6. Tm = 487.5 °C

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