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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
hot reservoircold reservoirEQH​ = 2200 kJQL​ = 1650 kJW

A heat engine takes in 2200 kJ of heat from a hot reservoir and rejects 1650 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2200 kJQL = 1650 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 7.48 kWẆ = 2.2 kW

A refrigerator removes heat from its cold space at a rate of 7.48 kW while its compressor uses 2.2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 7.48 kWẆ = 2.2 kW
Q̇H = kW
3.Medium
TH​ = 200 °CTL​ = 20 °CEQH​ = 2900 kJQL​W = ?

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 20 °C. It takes in 2900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 200 °CTL = 20 °CQH = 2900 kJ
Wmax = kJ
4.Medium
TH​ = 500 °CTL​ = 10 °CEQH​QL​η = 41%

A heat engine receives heat from a source at 500 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 41%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 500 °CTL = 10 °Cη = 41%
ηII = %
5.Hard
TH​ = 21 °CTL​ = 0 °CHPQ̇H​ = 14 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is 0 °C outside, delivering 14 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = 0 °CQ̇H = 14 kW
COPmax =
6.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 11 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -5 °CQ̇H = 11 kW
Ẇmin = kW

Answer key

  1. 1. η = 25 %
  2. 2. Q̇H = 9.68 kW
  3. 3. Wmax = 1103 kJ
  4. 4. ηII = 64.69 %
  5. 5. COPmax = 14.01
  6. 6. Ẇmin = 0.9723 kW

Full step-by-step solutions: practise this topic on examproblems.com.