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
kitchencold spaceRQ̇H​Q̇L​ = 3.3 kWẆ = 1.1 kW

A refrigerator removes heat from its cold space at a rate of 3.3 kW while its compressor uses 1.1 kW of power. Find its coefficient of performance COPR.

Q̇L = 3.3 kWẆ = 1.1 kW
COPR =
2.Easy
hot reservoircold reservoirEQH​ = 3900 kJQL​ = 2145 kJW = ?

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2145 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3900 kJQL = 2145 kJ
W = kJ
3.Medium
TH​ = 250 °CTL​ = 15 °CEQH​ = 800 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 15 °C. It takes in 800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 15 °CQH = 800 kJ
Wmax = kJ
4.Medium
TH​ = 500 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 500 °CTL = 30 °C
ηmax = %
5.Hard
TH​ = 28 °CTL​ = 5 °CRQ̇H​Q̇L​ = 1 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 28 °C, removing heat from the cold space at 1 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = 5 °CQ̇L = 1 kW
Ẇmin = kW
6.Hard
TH​ = 20 °CTL​ = 5 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 5 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 5 °CQ̇H = 14 kW
Ẇmin = kW

Answer key

  1. 1. COPR = 3
  2. 2. W = 1755 kJ
  3. 3. Wmax = 359.4 kJ
  4. 4. ηmax = 60.79 %
  5. 5. Ẇmin = 0.08269 kW
  6. 6. Ẇmin = 0.7164 kW

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