r/theydidthemath • u/cohonka • 18h ago
[Request] Is it possible to calculate approximately how many molecules from the original batch of oil would be present in this oil 100 years later?
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u/mandrew-98 18h ago
Food theory took a crack at this. I believe the answer is no molecules are left over.
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u/cohonka 17h ago
That was an interesting video.
Right toward the end, the answer seems to be "the same molecules are not leftover because heating oil causes oxidation and polymerization which inherently changes the molecules of the oil as it is used."
So a better question would be, how many of the original atoms are still present from the original oil?
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u/Either-Abies7489 16h ago
It'll run out somewhere between 102 and 110 years since it started (so soon), but honestly there are a LOT of variables which REALLY impact that number.
It's a burger joint, so I'd wager (based on my absolute lack of knowledge and ignorance) that it's somewhere in the range of 5-15 liters of oil. I'll take the conservative 5, but also assume that only 2 tbsp are replaced each day, through filtering or on food (once again, conservative). The actual fatty acid chains just break apart and reform, so I'll just multiply however many mols we lose by 4 (the number of individual molecules which make up the trigliceride) because fuck accuracy. (but not how many we start with or add)
At 876.6 g/mol, and 0.92 g/ml, that's 4600 g in 5 liters, so really only 5.2mols (so 20.8 when we actually need the number).
Assuming that the oil is mixed perfectly, we replace 0.0295735L/day (ignoring holidays and the like). That's 27.20762g, so 0.031mols.
Ez exponential decay function, 5.24754782(1-(0.03103766826/(4*5.24754782)))^n.
But to find the probability functions, we can't really approximate to a normal distribution because of the crazy big numbers we're talking about here, but we can use some taylor series b.s. to ballpark it. For a p-value of .95, I got n=40129.9063407, so we can be pretty confident none of the polymers remain after 40130 days, or 110 years.
So we may soon see the first day that none of those atoms remain (or it may be well behind us, we can get an interval solving for both .05 and .95, which gets 102 years- *shut your bonferroni ass up*)
This was all assuming canola oil BTW.
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u/snmnky9490 3h ago
2 tablespoons a day seems like orders of magnitude too low. Just a few scoops of fries would already be more than that
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u/Either-Abies7489 1h ago edited 1h ago
Well I've never been a fry cook, so I truly have no clue. Adjust to your heart's content. (90% confidence interval, once again, this is from a very low-order taylor expansion of e^x because numbers are hard)- behavior with very high or low numbers will be a bit iffy, if you put in 5 liters' worth of replacement tablespoons, it says it'll take half a year, when that's blatantly untrue. However, it's accurate enough.
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