I want to chime in on some of the technical talk. I am an engineer with an advanced degree and my work involves applications of the ideal gas laws and law of partial pressures (both fundamental building blocks of applied thermodynamics). The previous analyses are correct based on my understanding but there is a little more nuance that you can consider.
What the analysis above focused on is the change in pressure inside the ball when there is a change in the temperature outside the ball. Absolutely correct that the air inside will achieve thermal equilibrium with the ambient temperature outside the ball and the change in pressure will be roughly proportional to the change in temperature just how described (I say roughly because no real gas will behave exactly as an ideal gas but in this case, close enough for approximations).
It is also possible to manipulate the pressure inside the ball by taking advantage of the fact that the temperature of a gas will increase with an increase in pressure. When a ball is pumped up (pressure increased) that action will immediately increase the temperature according to the same ratios that the pressure changes as a result of temperature change.
So immediately after a ball is pumped up to say 12.5 psig (the g referring to gage pressure), the air inside the ball will be hotter than the ambient air (ambient air is at a pressure of 0 psig so it increases in temperature when squeezed to 12.5 psig and will increase the temperature of the air in the ball when mixed with whatever air is already in the ball and at ambient temperature). If the ref checked the pressure shortly after that (before it cooled), the pressure would be fine but the temperature inside the ball would be still warmer (maybe 10F warmer than ambient, depending on how much air was added). Then when taken outside, the pressure would reduce even further than predicted above.
Now I recognize that this does not explain why the Pats balls were soft and the Colts balls were not but it illustrates how a knowledgeable and devious person could manipulate the pressure in the balls without tampering with the balls after the refs inspected them.
One other point, someone said that moisture could condense out and impact pressure. This is true but the partial pressure of the water in the air at 70F say 30% RH is only about 0.25 psia. This is the total amount that the partial pressure of the water vapor contributes to the total pressure of 14.7 psia of the air-water mixture (atmospheric pressure). So even if half the water condensed out, it would make only a miniscule of difference per Dalton’s Law of Partial Pressures.
Wow, Celtics and Thermodynamics talk in the same place, a little slice of heaven for me. As for my theory of what really went on?, I think the trainers and maybe others figured out a way to manipulate the pressure in the balls without actually "tampering" with them after the refs inspected them. So is this breaking any rules, maybe not technically (good luck to the NFL trying to prove it anyway) but certainly it is circumventing the intent of the rules.
Thanks, Vermont Celtic. I love reading about this stuff.
The discrepancy in ball pressure between the Colt footballs and the Pats footballs will have to await further factual information. For example, is it not conceivable that Tom Brady selected balls at the low end of acceptable range (12.5) while Luck selected balls in the higher end (13.5), which could go toward explaining why the tested Pats balls fell below but the Colt footballs stayed within range. Did the Colt balls continue to test out at 13.5 during the game? Or closer to 12.5? And what range did the Pats' footballs test at during the game? Did 11 of the 12 balls test out at 10.5, which is what Chris Mortensen reported, or did it range from just under 12.5 to 10.5? I have heard there are conflicting reports on this. Sure wish the NFL would clarify this point.
Also just learned that the initial report from an Indy reporter, that this all got triggered by an interception in the 2nd quarter, in which the incriminating ball was turned over, is incorrect. Reports now state that the corrected balls were switched into the game BEFORE the interception. This does not affect the scientific analysis you astutely provided. But it does underscore how much misinformation and speculation is floating around.
I think the League is correct to take their time to analyze all the facts before they make any final determination, and I certainly hope that the Pats are exonerated. If it means letting the Patriots twist in the wind throughout the build up to the Super Bowl, well, I think that is okay too, kind of an additional payback on behalf of the disgruntled masses for the perception that Spygate was inadequately punished back in '07. The great irony, of course, could be if the accusations serve to motivate the team into even higher levels of performance, not at all outside the realm of possibility. And let's face it: if the Pats were to trounce the Seahawks, the mass of skeptics will be lining up the excuses as to how it could have happened, leaving off the list any suggestion that they are, in fact, a really, really good team.
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