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
C_{8}H_{18} + 16O_{2} ------> 8CO_{2} + 16H_{2}O
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^{o}C then there will be 0.6/22.4 = 0.03 mols of O_{2} for each intake stroke.
2. How many mols of Octane does this correspond to?
Answer: from the equation above there are 16 mols of O_{2} 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 0.169×5.5×10^{6}=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)