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
houseoutside airHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.6 delivers 19.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.6Q̇H = 19.5 kW
Ẇ = kW
2.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 4.92 kWẆ = 1.2 kW

A refrigerator removes heat from its cold space at a rate of 4.92 kW while its compressor uses 1.2 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 4.92 kWẆ = 1.2 kW
Q̇H = kW
3.Medium
TH​ = 725 °CTL​ = 25 °CEQH​QL​W

A heat engine works between a hot reservoir at 725 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency ηmax.

TH = 725 °CTL = 25 °C
ηmax = %
4.Medium
TH​ = 750 °CTL​ = 40 °CEQH​QL​η = 52%

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 52%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 750 °CTL = 40 °Cη = 52%
ηII = %
5.Hard
TH​ = 55 °CTL​ = -10 °CHPQ̇H​ = 13 kWQ̇L​Ẇ = ?

A heat pump delivers 13 kW of heat to a heating system at 55 °C, taking heat from a source at -10 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = -10 °CηII = 60%Q̇H = 13 kW
Ẇ = kW
6.Hard
TH​ = 850 °CTL​ = 35 °CEQH​ = 4100 kJQL​ = 1722 kJW = 2378 kJ

A heat engine takes in 4100 kJ of heat from a reservoir at 850 °C, produces 2378 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 850 °CTL = 35 °CQH = 4100 kJW = 2378 kJ
Sgen = kJ/K

Answer key

  1. 1. Ẇ = 4.239 kW
  2. 2. Q̇H = 6.12 kW
  3. 3. ηmax = 70.13 %
  4. 4. ηII = 74.93 %
  5. 5. Ẇ = 4.292 kW
  6. 6. Sgen = 1.938 kJ/K

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