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
kitchencold spaceRQ̇H​ = ?Q̇L​ = 0.72 kWẆ = 0.3 kW

A refrigerator removes heat from its cold space at a rate of 0.72 kW while its compressor uses 0.3 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 0.72 kWẆ = 0.3 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 2500 kJQL​ = 1375 kJW = ?

A heat engine takes in 2500 kJ of heat from a hot reservoir and rejects 1375 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2500 kJQL = 1375 kJ
W = kJ
3.Medium
TH​ = 400 °CTL​ = 40 °CEQH​QL​η = 32%

A heat engine receives heat from a source at 400 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 32%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 400 °CTL = 40 °Cη = 32%
ηII = %
4.Medium
TH​ = 625 °CTL​ = ?EQH​ = 1900 kJQL​ = 684 kJW

A reversible (Carnot) heat engine takes in 1900 kJ of heat from a reservoir at 625 °C and rejects 684 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 625 °CQH = 1900 kJQL = 684 kJ
TL = °C
5.Hard
800 °CTm​ = ?20 °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 20 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 800 °CTL = 20 °C
Tm = °C
6.Hard
TH​ = 20 °CTL​ = 5 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 5 °C outside, delivering 9 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 5 °CQ̇H = 9 kW
Ẇmin = kW

Answer key

  1. 1. Q̇H = 1.02 kW
  2. 2. W = 1125 kJ
  3. 3. ηII = 59.84 %
  4. 4. TL = 50.18 °C
  5. 5. Tm = 287.7 °C
  6. 6. Ẇmin = 0.4605 kW

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