Using the ideal gas law, and assuming the volume of the footballs stay the same, then
if the balls were inflated to 12.5 psi in an 80 degree room, then were brought outside to 20 degree conditions, then the ball pressure would be reduced to 11.1 psi.
P1=12.5 psi
T1=80 F = 299.8 K
T2=20 F = 266.5 K
P1/T1 = P2/T2
P2 = P1 (T2/T1) = 12.5 psi x (266.5 K / 299.8 K) = 11.1 psi
kidd’s conclusion: The cold air alone would account for 1.4 psi of the 2 psi underinflation. I doubt that pressure gages were used with enough accuracy to make a case that the balls were purposely underinflated.
I would guess that the Colts balls were equally deflated.
Under further review, there is not enough evidence to overturn the ruling on the field. The Colts are charged with a lost game.
my mistake
those are gage pressures
P1=12.5 psi(gage) = 27.2 psi (absolute)
T1=80 F = 299.8 K
T2=20 F = 266.5 K
P1/T1 = P2/T2
P2 = P1 (T2/T1) = 27.2 psi x (266.5 K / 299.8 K) = 24.18 psi (absolute) = 9.5 psi (gage)
Conclusion: The cold temperature accounts for ALL of the underinflation.
The basis for your calculations is wrong. It was 51º at kick off time.
Also, is there some “magic math” to explain why, in the same environment, the Patriots’ balls were under inflated, while the Seahawks’ balls were not?