Just fill the ball with warm humid indoor air, then when it temperature-equalizes with the 25°F cooler outdoor air on your AFC Championship playing field some of the water vapor in the ball will condense into water, leaving less air in the ball, solving the great mystery: how did the footballs used by the Championship winning New England Patriots show 12.5 psi of inflation pressure in the official pre-game check but only 10.5 psi when checked at halftime?
There is also a decrease in pressure due to the cooling of the molecules that remain gaseous. Those air molecules are not zipping around as fast as they were so they exert less outward pressure on the ball. But according to the ideal gas law, if there were no reduction in the number of gas molecules in the balls it would have taken a large drop in temperature, about 40°F, to cause the observed drop in air pressure. So says Boston College professor Martin Schmaltz:
In order for a ball to register a 10.5 PSI in a 50 degree environment [the temperature on the field at halftime] but register a 12.5 PSI in the testing environment, the ball would have to have been inflated, stored, and/or tested in a 91 degree environment.
I verify Schmaltz’s calculations at the end of this post, and while I’m no expert in the field, I get the same answer he does.
It wouldn’t be hard to deliver balls to the pre-game pressure check with 91° air inside. Just inflate them in a 100° sauna shortly before testing, but the Patriots are adamant that they do not know why the air pressure in their balls was low at halftime and if they had inflated their game balls in a sauna they would certainly know it.
The Carnegie Mellon experiment
An experiment performed by a team at Carnegie Mellon provides empirical support for the Patriots’ claim to have done nothing unusual. The Carnegie experimentalists inflated a batch of footballs to 12.5 psi at a room temperature of 75°F, then let the balls equalize to a new ambient temperature of 50°F, resulting in an average pressure drop of 1.8 psi. (They also wet the leather balls to simulate the rainy conditions of the game, surmising that this might allow stretching that would reduce air pressure in the ball, but this seems likely to be a minor factor.) The Carnegie experiment is video-documented here:
So how to account for the difference between the Carnegie findings and the ideal gas law, which predicts that a much larger decrease in temperature would be needed to create the observed pressure drop? Barring experimental error, it seems that the difference would have to be explained by condensation. Gas was removed from the ball, not via an inflation needle but by conversion to liquid water. What do our blog-reading experts say? Is this the likely explanation?
