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​ = 3400 kJQL​ = 2380 kJW = ?

A heat engine takes in 3400 kJ of heat from a hot reservoir and rejects 2380 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3400 kJQL = 2380 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 4100 kJQL​ = 2870 kJW

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 2870 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4100 kJQL = 2870 kJ
η = %
3.Medium
TH​ = 250 °CTL​ = 5 °CEQH​ = 1700 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 5 °C. It takes in 1700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 5 °CQH = 1700 kJ
Wmax = kJ
4.Medium
TH​ = 350 °CTL​ = 40 °CEQH​ = 900 kJQL​W = ?

A heat engine works between a hot reservoir at 350 °C and a cold reservoir at 40 °C. It takes in 900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 350 °CTL = 40 °CQH = 900 kJ
Wmax = kJ
5.Hard
TH​ = 950 °CT0​ = 25 °CTL​ = -15 °CERWQ̇H​ = 30 kWQ̇L​ = ?

A Carnot heat engine receives 30 kW of heat from a source at 950 °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 -15 °C and also rejects heat to the surroundings at 25 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 950 °CT0 = 25 °CTL = -15 °CQ̇H = 30 kW
Q̇L = kW
6.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 8 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 8 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = -10 °CQ̇H = 8 kW
COPmax =

Answer key

  1. 1. W = 1020 kJ
  2. 2. η = 30 %
  3. 3. Wmax = 796.1 kJ
  4. 4. Wmax = 447.7 kJ
  5. 5. Q̇L = 146.4 kW
  6. 6. COPmax = 9.772

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