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​ = 12.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.2 delivers 12.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.2Q̇H = 12.5 kW
Q̇L = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 50%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 50%
Q̇H = MW
3.Medium
TH​ = 400 °CTL​ = 15 °CEQH​QL​η = 31%

A heat engine receives heat from a source at 400 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 31%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 400 °CTL = 15 °Cη = 31%
ηII = %
4.Medium
TH​ = 425 °CTL​ = 30 °CEQH​ = 2600 kJQL​W = ?

A heat engine works between a hot reservoir at 425 °C and a cold reservoir at 30 °C. It takes in 2600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 425 °CTL = 30 °CQH = 2600 kJ
Wmax = kJ
5.Hard
TH​ = 45 °CTL​ = 7 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump delivers 14 kW of heat to a heating system at 45 °C, taking heat from a source at 7 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = 7 °CηII = 55%Q̇H = 14 kW
Ẇ = kW
6.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 18.5 kWQ̇L​Ẇ = ?

A heat pump delivers 18.5 kW of heat to a heating system at 22 °C, taking heat from a source at 7 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 7 °CηII = 50%Q̇H = 18.5 kW
Ẇ = kW

Answer key

  1. 1. Q̇L = 9.524 kW
  2. 2. Q̇H = 400 MW
  3. 3. ηII = 54.2 %
  4. 4. Wmax = 1471 kJ
  5. 5. Ẇ = 3.04 kW
  6. 6. Ẇ = 1.88 kW

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