[stupac2]

OK, let's do the math.  Here are the known facts:

Temperature at Gameday was 51 degrees F, which is 283.7 K

The pressure minimum is 12.5 psi (86 kPA)

The pressure in 11 of the 12 balls was found to be 2 PSI below the minimum pressure, which would be 10.5 psi (72.4 kPA)

Assuming that the volume of a football is fixed*, then we know that P/T must be a constant, which we know from the halftime measurement is  72.4 KPa/283.7 K = 0.255 KPa/degK.

If those balls were inspected 2 hrs before the game, and barely passed with 12.5 pSI (86 kPA), then the internal temperature must have been at least 86 kPa/0.255/degK = 336.5 K, which is 63 degrees C, which is 146 degrees F.

No amount of handling the football, unless they put it in an oven, would have gotten the internal temperature up to 146 degrees.

BC

* Note, the volume of the football is probably slightly dependent on the pressure, so the volume would have been lower at the lower pressure.  That means that the temperature would have had to be even higher than 146 F for the balls to pass the inspection.  Basically, I can see only a few possible ways that the observed facts could have happened.  The assumption of fixced volume, therefore, is conservative.

1) The balls were underpressured when they were inspected before the game, and the referees didn't really pay attention.

2) The balls were heated to 60+ degrees C right before the inspection so they could pass the inspection, and then naturally cooled and the pressure dropped.  60 degrees would have been noticeably hot, and this approach ran the risk that the balls cooled enough to drop below the minimum.  But if this is what happened, the Pats found a way to legally get around the letter of the law, if not the spirit.

3) At some point between inspection and halftime, air was let out of the balls.

I'm willing to entertain other explanations, but gameday temperature alone cannot explain the results.  Sorry.

BC

This is wrong. You're measuring gauge pressure, when what you care about is absolute pressure.* You need to add in atmospheric pressure, for the same reason you can't use F in the calculations. Atmospheric pressure is around 14.5 PSI, meaning instead of 10.5/12.5 you're doing 25/27, which means the drop is more like 8%. The change in temperature is about 4% so it's still higher, but is it so hard to believe that you can get another 4% change out of rubbing/evaporative cooling/whatever else? Anyway, since an unaffiliated lab actually did the experiment and found the 2 PSI change, are you calling them incompetent or liars? I can get not trusting the Patriots staff, but seriously? Read that link.


*Incidentally, I wasn't able to convince myself of this until the morning, and my main mental block was that footballs (and tires, and basically everything you pressurize with a pump) is a bladder of some sort so it expands. Think instead of a completely sealed metal box, no expansion. You open it to the atmosphere, seal it, then put your pump on it. Does the pump read 14.5 PSI? No, it doesn't. But if you're doing the gas law calculations, that's the pressure in there, very clearly. I mean, it's not 0, there are atoms in there, but the gauge is reading 0! It's because the gauge is telling you what you normally care about, which is pressure relative to the outside environment, but what you actually care about here is the absolute pressure, which no gauge (unless you work with vacuum systems) will tell you.

[stupac2]

OK, let's do the math.  Here are the known facts:

Temperature at Gameday was 51 degrees F, which is 283.7 K

The pressure minimum is 12.5 psi (86 kPA)

The pressure in 11 of the 12 balls was found to be 2 PSI below the minimum pressure, which would be 10.5 psi (72.4 kPA)

Assuming that the volume of a football is fixed*, then we know that P/T must be a constant, which we know from the halftime measurement is  72.4 KPa/283.7 K = 0.255 KPa/degK.

If those balls were inspected 2 hrs before the game, and barely passed with 12.5 pSI (86 kPA), then the internal temperature must have been at least 86 kPa/0.255/degK = 336.5 K, which is 63 degrees C, which is 146 degrees F.

No amount of handling the football, unless they put it in an oven, would have gotten the internal temperature up to 146 degrees.

BC

* Note, the volume of the football is probably slightly dependent on the pressure, so the volume would have been lower at the lower pressure.  That means that the temperature would have had to be even higher than 146 F for the balls to pass the inspection.  Basically, I can see only a few possible ways that the observed facts could have happened.  The assumption of fixced volume, therefore, is conservative.

1) The balls were underpressured when they were inspected before the game, and the referees didn't really pay attention.

2) The balls were heated to 60+ degrees C right before the inspection so they could pass the inspection, and then naturally cooled and the pressure dropped.  60 degrees would have been noticeably hot, and this approach ran the risk that the balls cooled enough to drop below the minimum.  But if this is what happened, the Pats found a way to legally get around the letter of the law, if not the spirit.

3) At some point between inspection and halftime, air was let out of the balls.

I'm willing to entertain other explanations, but gameday temperature alone cannot explain the results.  Sorry.

BC

This is wrong. You're measuring gauge pressure, when what you care about is absolute pressure.* You need to add in atmospheric pressure, for the same reason you can't use F in the calculations. Atmospheric pressure is around 14.5 PSI, meaning instead of 10.5/12.5 you're doing 25/27, which means the drop is more like 8%. The change in temperature is about 4% so it's still higher, but is it so hard to believe that you can get another 4% change out of rubbing/evaporative cooling/whatever else? Anyway, since an unaffiliated lab actually did the experiment and found the 2 PSI change, are you calling them incompetent or liars? I can get not trusting the Patriots staff, but seriously? Read that link.


*Incidentally, I wasn't able to convince myself of this until the morning, and my main mental block was that footballs (and tires, and basically everything you pressurize with a pump) is a bladder of some sort so it expands. Think instead of a completely sealed metal box, no expansion. You open it to the atmosphere, seal it, then put your pump on it. Does the pump read 14.5 PSI? No, it doesn't. But if you're doing the gas law calculations, that's the pressure in there, very clearly. I mean, it's not 0, there are atoms in there, but the gauge is reading 0! It's because the gauge is telling you what you normally care about, which is pressure relative to the outside environment, but what you actually care about here is the absolute pressure, which no gauge (unless you work with vacuum systems) will tell you.