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
hot reservoircold reservoirEQH​ = 4700 kJQL​ = 3525 kJW = ?

A heat engine takes in 4700 kJ of heat from a hot reservoir and rejects 3525 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4700 kJQL = 3525 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 10.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.7 delivers 10.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.7Q̇H = 10.5 kW
Ẇ = kW
3.Medium
TH​ = 475 °CTL​ = 30 °CEQH​ = 1400 kJQL​W = ?

A heat engine works between a hot reservoir at 475 °C and a cold reservoir at 30 °C. It takes in 1400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 475 °CTL = 30 °CQH = 1400 kJ
Wmax = kJ
4.Medium
TH​ = 750 °CTL​ = 40 °CEQH​QL​η = 49%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 49%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 40 °Cη = 49%
ηII = %
5.Hard
550 °CTm​ = ?25 °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 25 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 550 °CTL = 25 °C
Tm = °C
6.Hard
TH​ = 21 °CTL​ = 7 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 7 °C outside, delivering 13 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 7 °CQ̇H = 13 kW
Ẇmin = kW

Answer key

  1. 1. W = 1175 kJ
  2. 2. Ẇ = 2.234 kW
  3. 3. Wmax = 832.7 kJ
  4. 4. ηII = 70.61 %
  5. 5. Tm = 222.3 °C
  6. 6. Ẇmin = 0.6187 kW

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