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​ = 19 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.3 delivers 19 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.3Q̇H = 19 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 1800 kJQL​ = 1170 kJW

A heat engine takes in 1800 kJ of heat from a hot reservoir and rejects 1170 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1800 kJQL = 1170 kJ
η = %
3.Medium
TH​ = 275 °CTL​ = ?EQH​ = 3500 kJQL​ = 1840 kJW

A reversible (Carnot) heat engine takes in 3500 kJ of heat from a reservoir at 275 °C and rejects 1840 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 275 °CQH = 3500 kJQL = 1840 kJ
TL = °C
4.Medium
TH​ = 500 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 500 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 500 °CTL = 10 °C
ηmax = %
5.Hard
TH​ = 22 °CTL​ = 2 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 2 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 2 °CQ̇H = 6 kW
Ẇmin = kW
6.Hard
800 °CTm​ = ?30 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 800 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 30 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 800 °CTL = 30 °C
Tm = °C

Answer key

  1. 1. Q̇L = 14.58 kW
  2. 2. η = 35 %
  3. 3. TL = 15.02 °C
  4. 4. ηmax = 63.38 %
  5. 5. Ẇmin = 0.4066 kW
  6. 6. Tm = 297.2 °C

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