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​ = 1900 kJQL​ = 1520 kJW

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1520 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1900 kJQL = 1520 kJ
η = %
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 6.08 kWẆ = 1.6 kW

A refrigerator removes heat from its cold space at a rate of 6.08 kW while its compressor uses 1.6 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 6.08 kWẆ = 1.6 kW
Q̇H = kW
3.Medium
TH​ = 400 °CTL​ = 20 °CEQH​QL​W

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency ηmax.

TH = 400 °CTL = 20 °C
ηmax = %
4.Medium
TH​ = 20 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 7 kWẆ

A reversible refrigerator keeps a cold room at -25 °C by removing 7 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -25 °CTH = 20 °CQ̇L = 7 kW
Q̇H = kW
5.Hard
TH​ = 28 °CTL​ = -10 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 28 °C, removing heat from the cold space at 2.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = -10 °CQ̇L = 2.5 kW
COPmax =
6.Hard
TH​ = 850 °CTL​ = 40 °CEQH​ = 4600 kJQL​ = 2300 kJW = 2300 kJ

A heat engine takes in 4600 kJ of heat from a reservoir at 850 °C, produces 2300 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 850 °CTL = 40 °CQH = 4600 kJW = 2300 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 20 %
  2. 2. Q̇H = 7.68 kW
  3. 3. ηmax = 56.45 %
  4. 4. Q̇H = 8.269 kW
  5. 5. COPmax = 6.925
  6. 6. Sgen = 3.249 kJ/K

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