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​ = 12.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.4 delivers 12.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.4Q̇H = 12.5 kW
Ẇ = kW
2.Easy
kitchencold spaceRQ̇H​Q̇L​ = 8.96 kWẆ = 2.8 kW

A refrigerator removes heat from its cold space at a rate of 8.96 kW while its compressor uses 2.8 kW of power. Find its coefficient of performance COPR.

Q̇L = 8.96 kWẆ = 2.8 kW
COPR =
3.Medium
TH​ = 275 °CTL​ = 15 °CEQH​ = 1900 kJQL​W = ?

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 15 °C. It takes in 1900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 275 °CTL = 15 °CQH = 1900 kJ
Wmax = kJ
4.Medium
TH​ = 200 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 200 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 32 °CTL​ = -25 °CRQ̇H​Q̇L​ = 5 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 32 °C, removing heat from the cold space at 5 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -25 °CQ̇L = 5 kW
Ẇmin = kW
6.Hard
550 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 550 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 40 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 550 °CTL = 40 °C
Tm = °C

Answer key

  1. 1. Ẇ = 3.676 kW
  2. 2. COPR = 3.2
  3. 3. Wmax = 901.2 kJ
  4. 4. ηmax = 41.21 %
  5. 5. Ẇmin = 1.148 kW
  6. 6. Tm = 234.6 °C

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