ESPN analysts want deflategate to be as big a controversy as possible but science gives us another option. Much like how Fox News denounces science in the face of evolution, I’m sure you’ll never hear a Mothership mouth bring up Gay-Lussac’s law.
We were tipped off to this post written by a science professor by the Boston Globe which reads,
Given the conditions of the game, a ball which meets specifications in the locker room could easily lose enough pressure to be considered under-inflated. Some math:
*Guy-Lussac’s Law describes the relationship between the pressure of a confined ideal gas and its temperature. For the sake of argument, we will assume that the football is a rigid enough container (unless a ball is massively deflated, it’s volume won’t change). The relationship is (P1/T1) = (P2/T2), where P is the pressure and T is the temperature in Kelvins.
*The balls are inflated to between 12.5 and 13.5 psi at a temperature of 70 degrees Farenheit (294.1 K). Let’s assume an average ball has a gauge pressure of 13 psi. This makes the absolute pressure of the ball 27.7 psi (gauge + atmosphere). Since these are initial values, we will call them P1 and T1.
*The game time temperature was 49 degrees F (278 K). We are attempting to solve for the new pressure at this temperature, P2. We plug everything into the equation and get (27.7/294.1) = (P2/278). At the game time temperature, the balls would have an absolute pressure of 26.2 psi and a gauge pressure of 11.5, below league specifications.
**Furthermore, given that it was raining all day, the air in the stadium was saturated with water vapor. At 70 degrees, water has a vapor pressure of 0.38 psi. The total pressure of the ball is equal to the pressure of the air inside the ball and the vaporized water in the ball. At 49 degrees, the vapor pressure of water is 0.13 psi. Up to 0.25 additional psi can be lost if the balls were inflated by either the team or the refs prior to the game. Granted, it’s unlikely that anyone would inflate balls from 0, but it easily could cost another couple hundredths of a psi in pressure.
For a ball that barely meets specifications (12.5 psi gauge), it’s pressure would drop to 11.1 psi during the game… enough to be considered massively underinflated.
That being said, you can count on ESPN sticking to their story because after all, it’s not about the science your in your brain, it’s about what your heart tells you in your gut.