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​ = 3300 kJQL​ = 1980 kJW

A heat engine takes in 3300 kJ of heat from a hot reservoir and rejects 1980 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3300 kJQL = 1980 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 2000 kJQL​ = 1100 kJW

A heat engine takes in 2000 kJ of heat from a hot reservoir and rejects 1100 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2000 kJQL = 1100 kJ
η = %
3.Medium
TH​ = 28 °CTL​ = -20 °CRQ̇H​ = ?Q̇L​ = 8.5 kWẆ

A reversible refrigerator keeps a cold room at -20 °C by removing 8.5 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -20 °CTH = 28 °CQ̇L = 8.5 kW
Q̇H = kW
4.Medium
TH​ = 600 °CTL​ = ?EQH​ = 600 kJQL​ = 219 kJW

A reversible (Carnot) heat engine takes in 600 kJ of heat from a reservoir at 600 °C and rejects 219 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 600 °CQH = 600 kJQL = 219 kJ
TL = °C
5.Hard
TH​ = 600 °CT0​ = 30 °CTL​ = -20 °CERWQ̇H​ = 20 kWQ̇L​ = ?

A Carnot heat engine receives 20 kW of heat from a source at 600 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -20 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 600 °CT0 = 30 °CTL = -20 °CQ̇H = 20 kW
Q̇L = kW
6.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 5 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 5 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

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

Answer key

  1. 1. η = 40 %
  2. 2. η = 45 %
  3. 3. Q̇H = 10.11 kW
  4. 4. TL = 45.55 °C
  5. 5. Q̇L = 66.1 kW
  6. 6. COPmax = 11.31

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