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​ = 10 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.3 delivers 10 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.3Q̇H = 10 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.8 delivers 9 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.8Q̇H = 9 kW
Ẇ = kW
3.Medium
TH​ = 700 °CTL​ = 40 °CEQH​QL​η = 27%

A heat engine receives heat from a source at 700 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 27%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 700 °CTL = 40 °Cη = 27%
ηII = %
4.Medium
TH​ = 225 °CTL​ = ?EQH​ = 4100 kJQL​ = 2536 kJW

A reversible (Carnot) heat engine takes in 4100 kJ of heat from a reservoir at 225 °C and rejects 2536 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 225 °CQH = 4100 kJQL = 2536 kJ
TL = °C
5.Hard
TH​ = 22 °CTL​ = -5 °CHPQ̇H​ = 4 kWQ̇L​Ẇ

A heat pump keeps a house at 22 °C while it is -5 °C outside, delivering 4 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 22 °CTL = -5 °CQ̇H = 4 kW
COPmax =
6.Hard
TH​ = 22 °CTL​ = 0 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 0 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 0 °CQ̇H = 6 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 2.326 kW
  2. 2. Ẇ = 2.368 kW
  3. 3. ηII = 39.81 %
  4. 4. TL = 34.97 °C
  5. 5. COPmax = 10.93
  6. 6. Ẇmin = 0.4472 kW

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