ESPN is misinterpreting the ideal gas law. A game-time temperature of 51 degrees decreased football PSI by bout 6%.
The ideal gas law stats that pressure is directly proportional to temperature. Let's assume the temperature differential from locker room to field on the night of the 2014 AFCC game was 20 degrees Fahrenheit. The common perception is that a temperature change of 20 degrees represents a percent change of about 28.5% (this is found dividing the 20 degree drop by an original temperature of 70 degrees, resulting in 0.2857).
The problem is that the ideal gas law does only works in degrees Kelvin. Zero degrees Fahrenheit is not actually zero, it's 255 degrees Kelvin. The mathematics of the ideal gas law fails using Fahrenheit degrees because Fahrenheit is not a proportional scale.
If we assume a 20 degree Fahrenheit temperature differential, then the temperature changed from 326 Kelvin to 306 Kelvin. This results in a percent change of 6.1%. Therefore, according to the idea gas law, the balls should have been 6% deflated by halftime. What does this mean for PSI measure?
Here's a table of the measured pressure of each ball, adjusted to account for the ideal gas law.
Ball# PSI range
1 12.23 - 12.55
2 11.54 - 11.91
3 11.86 - 12.23
4 11.38 - 11.70
5 11.80 - 12.18
6 12.34 - 12.70
7 12.60 - 13.08
8 11.84 - 12.28
9 11.64 - 12.07
10 11.17 - 11.59
11 11.59 - 12.07
Now I am a die hard Patriots fan, but also a math teacher who holds a degree in physics. The science is fairly conclusive that these balls were under-inflated.
