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​ = 5.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.3 delivers 5.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.3Q̇H = 5.5 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 500 kJQL​ = 300 kJW

A heat engine takes in 500 kJ of heat from a hot reservoir and rejects 300 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 500 kJQL = 300 kJ
η = %
3.Medium
TH​ = 375 °CTL​ = ?EQH​ = 2600 kJQL​ = 1296 kJW

A reversible (Carnot) heat engine takes in 2600 kJ of heat from a reservoir at 375 °C and rejects 1296 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 375 °CQH = 2600 kJQL = 1296 kJ
TL = °C
4.Medium
TH​ = 300 °CTL​ = 15 °CEQH​QL​η = 32%

A heat engine receives heat from a source at 300 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 32%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 300 °CTL = 15 °Cη = 32%
ηII = %
5.Hard
TH​ = 650 °CT0​ = 20 °CTL​ = -10 °CERWQ̇H​ = 110 kWQ̇L​ = ?

A Carnot heat engine receives 110 kW of heat from a source at 650 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -10 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 20 °CTL = -10 °CQ̇H = 110 kW
Q̇L = kW
6.Hard
TH​ = 450 °CT0​ = 20 °CTL​ = -15 °CERWQ̇H​ = 160 kWQ̇L​ = ?

A Carnot heat engine receives 160 kW of heat from a source at 450 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 450 °CT0 = 20 °CTL = -15 °CQ̇H = 160 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 1.667 kW
  2. 2. η = 40 %
  3. 3. TL = 49.93 °C
  4. 4. ηII = 64.35 %
  5. 5. Q̇L = 658.5 kW
  6. 6. Q̇L = 701.7 kW

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