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
hot reservoircold reservoirEQH​ = 1500 kJQL​ = 900 kJW = ?

A heat engine takes in 1500 kJ of heat from a hot reservoir and rejects 900 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1500 kJQL = 900 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 12.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.3 delivers 12.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.3Q̇H = 12.5 kW
Q̇L = kW
3.Medium
TH​ = 450 °CTL​ = 5 °CEQH​ = 4800 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 5 °C. It takes in 4800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 5 °CQH = 4800 kJ
Wmax = kJ
4.Medium
TH​ = 425 °CTL​ = ?EQH​ = 2900 kJQL​ = 1259 kJW

A reversible (Carnot) heat engine takes in 2900 kJ of heat from a reservoir at 425 °C and rejects 1259 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 425 °CQH = 2900 kJQL = 1259 kJ
TL = °C
5.Hard
TH​ = 850 °CT0​ = 20 °CTL​ = -20 °CERWQ̇H​ = 160 kWQ̇L​ = ?

A Carnot heat engine receives 160 kW of heat from a source at 850 °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 -20 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 850 °CT0 = 20 °CTL = -20 °CQ̇H = 160 kW
Q̇L = kW
6.Hard
TH​ = 20 °CTL​ = -5 °CHPQ̇H​ = 9.5 kWQ̇L​Ẇ = ?

A heat pump delivers 9.5 kW of heat to a heating system at 20 °C, taking heat from a source at -5 °C. Its actual COP is 35% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 20 °CTL = -5 °CηII = 35%Q̇H = 9.5 kW
Ẇ = kW

Answer key

  1. 1. W = 600 kJ
  2. 2. Q̇L = 8.712 kW
  3. 3. Wmax = 2954 kJ
  4. 4. TL = 29.94 °C
  5. 5. Q̇L = 748.3 kW
  6. 6. Ẇ = 2.315 kW

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