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​ = 16 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.5 delivers 16 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.5Q̇H = 16 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 1900 kJQL​ = 1235 kJW = ?

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1235 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1900 kJQL = 1235 kJ
W = kJ
3.Medium
TH​ = 250 °CTL​ = 25 °CEQH​ = 3200 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 25 °C. It takes in 3200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 25 °CQH = 3200 kJ
Wmax = kJ
4.Medium
TH​ = 700 °CTL​ = 30 °CEQH​QL​η = 48%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 48%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 30 °Cη = 48%
ηII = %
5.Hard
TH​ = 30 °CTL​ = -25 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -25 °CQ̇L = 1.5 kW
Ẇmin = kW
6.Hard
TH​ = 700 °CT0​ = 25 °CTL​ = -25 °CERWQ̇H​ = 150 kWQ̇L​ = ?

A Carnot heat engine receives 150 kW of heat from a source at 700 °C and rejects heat to the surroundings at 25 °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 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 700 °CT0 = 25 °CTL = -25 °CQ̇H = 150 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 6.4 kW
  2. 2. W = 665 kJ
  3. 3. Wmax = 1376 kJ
  4. 4. ηII = 69.72 %
  5. 5. Ẇmin = 0.3325 kW
  6. 6. Q̇L = 516.4 kW

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