Tucsonan solves deflate-gate with engineering math

Patriots Manager Belichick got it right!

When a gas is enclosed in a confined space it will expand or contract, depending on temperature. We have seen this in our own lives when inflated balloons “wimp out” as the weather cools down.

This “law of nature” has been experimentally studied, and in 1834 was first stated by Clayeyron as a combination of Boyle’s Law and Charles’s Law. It is now known as the Ideal Gas Law.

The law is written as PV = nRT, where the letters denote pressure, volume, amount (n), and gas constant (R), of the gas respectively. Since, in a football, V and n are constant, and since R is a constant, we can simplify the gas law to P2 = P1 x (T2/T1), where subscripts 1 and 2 refer to the initial and final conditions, respectively.

Since air is close to ideal gas qualities, this law is sufficiently accurate to be used to determine a football’s pressure change vs temperature. The P and T in the above equation are modified forms of pounds per square inch and degrees F, due to the unique dimensions of the gas constant R.

If a ball initially has a pressure of 13 psi, the final ball pressure will be according to the table below:

(Note that when inserting pressure numbers into the equation, the pressures must be in “absolute” form by adding 14.7 to each of the measured (gage) pressures-for example, for 13 psi, 27.7 psi must be used; and then the 14.7 must be subtracted from the final pressure answer to get the final measured pressure)

All the above is meaningless if someone lets air out of the ball!!