The ideal gas law. Seems nothing is ideal since Obama first got elected.
The ideal gas law says that the pressure P times the volume V is equal to n the number of moles of gas contained in the volume times the universal gas constant R times the temperature T.
T is the temperature above absolute zero. P is the absolute pressure. The absolute pressure is the gauge pressure plus atmospheric pressure. I recall 1 standard atmospheric pressure to be 14.7 pounds per square inch.
Most solids, liquids, and gases expand with increasing temperature and contract with decreasing temperature.
Typically, gases expand(contract) more(less) than liquids which expand(contract) more than solids with increasing(decreasing) temperature.
In brief, both the leather of the football and the air in it should expand with temperature and contract with decreasing temperature.
Physicists usually consider the simplest model first. The simplest model is that the ideal gas law holds and that the only material affected by the temperature is the gas inside the football.
This model will assume that n and V are constant.
Any decrease in temperature will cause a ball inflated to 12.5 lbs/sqin to be outside the official range.
One atmosphere is 14.7 lbs/in**2. A minimally inflated ball should have an actual pressure of 27.2 lbs/sqin.
The temperature in Rankine is the temperature in Fahrenheit plus 459.67.
P2ndhalf =( P@inpection+14.7)* T2ndhalf/T@imspection.-14.7
Assume room temperature is 72 degrees F and the temperature at the beginning of the 2nd half was 51 degrees F.
Under these conditions, the pressure at the beginning of the 2nd half would be 11.43 lbs/sqin.
DR2H
I couldn't figure out all the machinations in the New York Times article because it didn't show all the work on the board, but it looked unnecessarily complicated to me. If we use the ideal gas law, and if the volume and the number of moles of gas are constant, then (Delta P)/P = (Delta T)/T. If we use an average temperature for T of (72 F +51 F)/2 +459 = 520 R and Delta T = 72-51= 21 R, then (Delta T)/T=.04. Assuming P = 12.5+14.7 = 27 PSI, then (Delta P) = 27 x .04 = 1.1 PSI. So the measured gauge pressure in the ball would be 12.5-1.1 = 11.4 PSI, in agreement with your analysis, and substantially more than the supposedly measured 10.5 PSI. It looks like monkey business to me. I couldn't figure out what was going on in the New York Times article, but it looked a whole lot more complicated than this. Did I miss something?
ReplyDeleteYou missed Tom Brady's hour plus news conference and that's about all.
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