Ferrari versus the 2nd Law

So what about real life, how well does the F1 Ferrari measure up when compared the the maximum efficiency?

Well the Ferrari engine has a total capacity of 3 litres and, according to them, produces ">750HP" at 12,000 revolutions per minute.

Considering the combustion of fuel as

 C₈H₁₈ + 16O₂ ------> 8CO₂ + 16H₂O 

where 5.5MJ is released per mole of octane as energy of combustion. 

To work it out follow the questions below - to reveal the answer just click over the question your working on.

• 1. How many molecules of Oxygen are taken in for each intake stroke? (Air is 20% Oxygen)

  • Answer: 20% of 3 litres is 0.6 litres.  As 1 mol of gas occupies 22.4 litres at 20^oC then there will be 0.6/22.4 = 0.03 mols of O₂ for each intake stroke.

• 2. How many mols of Octane does this correspond to?

  • Answer: from the equation above there are 16 mols of O₂ for every mol of octane so there are 0.03/16 = 1.69×10^-3 mols of octane burned for each intake stroke.

• 3. How much heat is input per second?

  • Answer: There is one intake stroke for every two revolutions.

  • 12,000 revolution/minute = 200 revolutions/s = 100 intake strokes/s.

  • 100×1.69×10^-3 = 0.169 mols of octane burned per second. 

  • Therefore 0.169×5.5×10⁶=929500J/s are produced this is 929500W.

• 4. Using gamma = 1.4 and a compression ratio of 12 calculate the expected efficiency of the Ferrari engine.

  • Answer: using  the expression from the last page this is 1-(1/12)^(1.4-1) = 0.63

• 5. Calculate the maximum power output (given1HP = 746W).

  • Answer: the max power possible is 0.63×929500 = 585585W

  • 585585/746 = 785HP

Therefore the maximum power a Ferrari engine could produce is 785HP and they say that it produces ">750HP" so as you may have guessed Ferrari are getting pretty near to perfect - that might explain why they just keep on winning.

(images taken, without permission, from http://www.formula1.com)