http://phys.org/news/2015-01-football-physics-science-deflategate.html
News reports say that 11 of the 12 game balls used by the New England Patriots in their AFC championship game against the Indianapolis Colts were deflated, showing about 2 pounds per square inch (psi) less pressure than the 13 psi required by the rules, so it seems that the most bizarre sports scandal of recent memory is real. But there are still plenty of questions: why would a team deflate footballs? Could there be another explanation? And most importantly, what does physics tell us about all this?
For New England fans, the first priority is a search for an innocent explanation. After all, party balloons and car tires deflate during cold winter weather, so might a simple temperature difference be responsible for the change in inflation pressure?
The physics principle known as the ideal gas law tells us that a reduction in temperature leads to a reduction in pressure. The pressure of a confined gas multiplied by its volume is proportional to the number of molecules in the gas multiplied by the temperature. Maybe you remember the equation PV=nRT from your schooldays. So if you cool a gas while keeping its volume fixed, the pressure must decrease.
But we don't need equations to check this: we can demonstrate it directly. I got a couple of old footballs from Union College's athletic department, pumped them up and popped them in the freezer. After a night in the cold, the pressure was around 2psi lower, just like the Patriots' footballs—from about 19psi at the start (I slightly overinflated the balls by using the tire pump in my car) down to about 17 psi.