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.

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1.Easy
kitchencold spaceRQ̇H​ = ?Q̇L​ = 7.44 kWẆ = 2.4 kW

A refrigerator removes heat from its cold space at a rate of 7.44 kW while its compressor uses 2.4 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 7.44 kWẆ = 2.4 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 2200 kJQL​ = 1540 kJW = ?

A heat engine takes in 2200 kJ of heat from a hot reservoir and rejects 1540 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2200 kJQL = 1540 kJ
W = kJ
3.Medium
TH​ = 325 °CTL​ = ?EQH​ = 2500 kJQL​ = 1288 kJW

A reversible (Carnot) heat engine takes in 2500 kJ of heat from a reservoir at 325 °C and rejects 1288 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 325 °CQH = 2500 kJQL = 1288 kJ
TL = °C
4.Medium
TH​ = 800 °CTL​ = ?EQH​ = 900 kJQL​ = 250 kJW

A reversible (Carnot) heat engine takes in 900 kJ of heat from a reservoir at 800 °C and rejects 250 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 800 °CQH = 900 kJQL = 250 kJ
TL = °C
5.Hard
TH​ = 28 °CTL​ = 5 °CRQ̇H​Q̇L​ = 1.5 kWẆ

A refrigerator keeps its cold space at 5 °C in a kitchen at 28 °C, removing heat from the cold space at 1.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = 5 °CQ̇L = 1.5 kW
COPmax =
6.Hard
TH​ = 20 °CTL​ = 10 °CHPQ̇H​ = 19 kWQ̇L​Ẇ = ?

A heat pump delivers 19 kW of heat to a heating system at 20 °C, taking heat from a source at 10 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = 10 °CηII = 30%Q̇H = 19 kW
Ẇ = kW

Answer key

  1. 1. Q̇H = 9.84 kW
  2. 2. W = 660 kJ
  3. 3. TL = 35.02 °C
  4. 4. TL = 24.95 °C
  5. 5. COPmax = 12.09
  6. 6. Ẇ = 2.16 kW

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