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​ = 4800 kJQL​ = 2880 kJW

A heat engine takes in 4800 kJ of heat from a hot reservoir and rejects 2880 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4800 kJQL = 2880 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 8.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.9 delivers 8.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.9Q̇H = 8.5 kW
Q̇L = kW
3.Medium
TH​ = 575 °CTL​ = ?EQH​ = 3700 kJQL​ = 1322 kJW

A reversible (Carnot) heat engine takes in 3700 kJ of heat from a reservoir at 575 °C and rejects 1322 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 575 °CQH = 3700 kJQL = 1322 kJ
TL = °C
4.Medium
TH​ = 800 °CTL​ = ?EQH​ = 3400 kJQL​ = 897 kJW

A reversible (Carnot) heat engine takes in 3400 kJ of heat from a reservoir at 800 °C and rejects 897 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 800 °CQH = 3400 kJQL = 897 kJ
TL = °C
5.Hard
TH​ = 300 °CTL​ = 35 °CEQH​ = 4700 kJQL​ = 3384 kJW = 1316 kJ

A heat engine takes in 4700 kJ of heat from a reservoir at 300 °C, produces 1316 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 300 °CTL = 35 °CQH = 4700 kJW = 1316 kJ
Sgen = kJ/K
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 highest possible coefficient of performance COPmax.

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

Answer key

  1. 1. η = 40 %
  2. 2. Q̇L = 6.765 kW
  3. 3. TL = 29.89 °C
  4. 4. TL = 9.972 °C
  5. 5. Sgen = 2.781 kJ/K
  6. 6. COPmax = 11.31

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