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​ = 2.8 kWẆ = 1 kW

A refrigerator removes heat from its cold space at a rate of 2.8 kW while its compressor uses 1 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.8 kWẆ = 1 kW
COPR =
2.Easy
hot reservoircold reservoirEQH​ = 1700 kJQL​ = 1360 kJW = ?

A heat engine takes in 1700 kJ of heat from a hot reservoir and rejects 1360 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1700 kJQL = 1360 kJ
W = kJ
3.Medium
TH​ = 250 °CTL​ = ?EQH​ = 4900 kJQL​ = 2605 kJW

A reversible (Carnot) heat engine takes in 4900 kJ of heat from a reservoir at 250 °C and rejects 2605 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 250 °CQH = 4900 kJQL = 2605 kJ
TL = °C
4.Medium
TH​ = 600 °CTL​ = 10 °CEQH​QL​η = 27%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 27%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 10 °Cη = 27%
ηII = %
5.Hard
TH​ = 35 °CTL​ = 5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump delivers 11 kW of heat to a heating system at 35 °C, taking heat from a source at 5 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 35 °CTL = 5 °CηII = 55%Q̇H = 11 kW
Ẇ = kW
6.Hard
TH​ = 700 °CTL​ = 20 °CEQH​ = 1500 kJQL​ = 765 kJW = 735 kJ

A heat engine takes in 1500 kJ of heat from a reservoir at 700 °C, produces 735 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 700 °CTL = 20 °CQH = 1500 kJW = 735 kJ
Sgen = kJ/K

Answer key

  1. 1. COPR = 2.8
  2. 2. W = 340 kJ
  3. 3. TL = 4.974 °C
  4. 4. ηII = 39.96 %
  5. 5. Ẇ = 1.947 kW
  6. 6. Sgen = 1.068 kJ/K

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