Deflate gate | Gases and kinetic molecular theory | Chemistry | Khan Academy

Deflate gate | Gases and kinetic molecular theory | Chemistry | Khan Academy


Ever since the AFC championship game,
and into the run-up to the Super Bowl, there’s been a lot of talk
about deflated footballs. And in particular, to what degree
can the pressure of a football go down– to what degree can it get deflated–
based on temperature differentials from where it was inflated
to where it is actually played. Especially if it’s inflated in a
warmer environment, say indoors, and then it’s played outdoors,
in a colder environment. And so to think about this, we’ll take out one of my
favorite laws or equations, the ideal gas law. And it tells us that
pressure times volume is equal to the number of molecules
of our ideal gas we’re dealing with– it’s measured in terms of moles, which is
the measure of the number of molecules– times our ideal gas constant,
times our temperature. Or if we just want to rearrange it–
and I do want to rearrange it, because I just want to
solve for P here– we can divide both sides by V,
and we would be left with P is equal to nRT over V. Now let’s think about
the exact case of what happened with the New England football– what the argument is for why
they might have deflated naturally– why there might not be foul play. The argument is maybe they were
inflated indoors where the temperature was room temperature–
so roughly 75 degrees Fahrenheit, which is roughly 24 degrees Celsius,
and in order to apply the ideal gas law, we’d want to convert it to Kelvin,
so this is approximately 297 Kelvin. That’s the indoor temperature. So if we’re infated here, indoors, and then we play outdoors, where the temperature is
roughly 50 degrees Fahrenheit– and that, from what I’ve read,
was actually the temperature on the field during
the New England game. 50 degrees Fahrenheit, which is
approximately 10 degrees Celsius, which is approximately 283 Kelvin. So the argument being made is,
look, you have this temperature drop, could that temperature drop, if this
temperature drops by a certain percent, could that account for the pressure drop
that was actually measured? And the pressure drop that was
actually measured, gauge pressure– and this is an important point,
because it was glossed over in some of the initial analyses– the gauge pressure indoors,
where the ball was inflated, was 12 point 5 pounds per square inch, and the gauge pressure outdoors,
where it was felt the balls were deflated somehow, or where they
had less pressure, was 10 point 6 pounds per square inch. So, to see if these numbers are
consistent with no foul play, let’s simplify our
ideal gas law a little bit– make it a little bit particular for this
circumstance. So in this circumstance,
we’re going to assume no foul play. If we assume no foul play,
that means no air is let into or out of. So the number of molecules
aren’t going to change. The ideal gas constant
obviously shouldn’t change, it’s a universal gas constant,
so this should be constant. And then our volume– let’s just assume the football is made
out of leather, it’s relatively rigid– its volume might have
changed a little bit, but for the sake of our analysis,
we’ll say that it pretty much held up its shape. So its volume stayed constant
as we went from indoors to outdoors. So to simplify this equation, let’s just
call all of this stuff in green K. If you take your n, multiply it times R,
divide it by V, that’s just equal to some constant called K. So we can simplify all of this to
P, pressure, in this case, should be some constant times temperature. Because once again, we’re assuming
volume doesn’t change, we’re assuming no air is let in or out. So when you look at it this way, any percent change on temperature should
have the same percent change in pressure. So let’s see if the percent change
in temperature is consistent with the percent change in pressure
that was actually observed. And so when we look at the temperature,
we should be doing it in Kelvin, so we should look at this change here,
going from 297 Kelvin to 283 Kelvin. So what is the drop here? Let’s see. It’s a drop of 14 Kelvin,
let me get my calculator out. It’s a drop of 14 Kelvin. And we started at 297, so divided by 297, let’s just say if we round
to the nearest percentage, gets us zero point zero four seven,
that’s rougly a five percent drop. So this is a five percent drop. And I’ll write approximately
5 percent drop. Now let’s see what
the drop in pressure is. So this is going from 12 point 5 psi
to 10 point 6 psi. That’s 1.9 psi drop. So that’s 1.9 psi drop
divided by our start, which is 12 point 5, which looks like a 15 point 2
percent drop, or roughly a 15 percent drop. So things are starting to look shady. This looks like a 15 percent drop. And this is actually what some of the
initial analyses did, they said, look, something
clearly shady happened, because temperature by itself
should only account for a 5 percent drop in pressure, but
there was a 15 percent drop in pressure, so maybe some air was let out somehow. But there was actually a mistake
in that initial analysis. Gauge pressure, the 12 point 5 psi,
that’s actually not the absolute pressure. What gauge pressure is a measure of is how much more pressure
you have inside than outside. Outside the ball, you do have pressure,
standard atmospheric pressure. And it might change depending on
the weather, et cetera. But there is pressure. The pressure is caused by
the weight of the atmosphere. So, in order to figure absolute pressure, and to figure out the correct
percentage change, you need to add how much
more pressure there is inside the ball to what the outside pressure is. And I don’t know the exact readings
for that day in New England, but standard atmospheric pressure
is 14 point 7 psi. So plus 14 point 7 psi gets us to, 27 point 2 psi. And if we add the 14 point 7 over here, again, to get the true absolute pressure– once again, the gauge reading is just
how much more pressure inside the football than outside. So if you want the true pressure,
the absolute pressure, you add these. And this is going to be 25 point 2 psi. Now we can calculate
the actual percentage drop, and compare it to this 5 percent drop. Minor mistake, this is 25 point 3 psi. So we still have the same drop, we have a 1 point 9 psi drop, to go from 27 point 2
to 25 point 3. But it’s over a larger base. So it should be a lower percentage. Let’s calculate what that is. We have 1 point 9 psi drop,
divided by 27 point 2 psi. Is equal to a little under
a seven percent drop. So approximately a seven percent drop. Now these two things are not exact. But they are a lot closer. And this degree, you’re like, okay, there might have been
other factors at play. Maybe some of the measurements
weren’t done exactly right. Maybe actually the ambient pressure was somehow different inside and outside. There’s also some possibility,
especially when you’re outside, that some water,
some precipitation is on the ball. As that precipitation evaporates, it might cool down the ball further, which would drop the pressure even more. So this isn’t definitive, but at least the numbers here,
when we apply the ideal gas law properly, they pretty much account for
most of the pressure drop. So at least here,
I wouldn’t get too caught up in all of the conspiracy theories.

61 Replies to “Deflate gate | Gases and kinetic molecular theory | Chemistry | Khan Academy”

  1. Great example of Scientific Sleuthing.  Love your Sherlock Holmes approach!  Love you man for you make up for the IQ loss of all the zombies tweeting around aimlessly!

  2. Ok, so how does this affect only a single team's balls?  Why was it only NE balls that were underflated? Even if it was the pressure and envionment?

  3. Assuming for the sake of argument that there was no foul play, why did this change in pressure not occur in ALL of the footballs?

  4. Hang on, now I have to laugh that this is remotely "cheating" against the Pats now.  Cheating would involve having an actual advantage, and when you include variance in these numbers, it's way too small for it to have any effect on any part of the game. XD

  5. Khan! you can do a basic statistical analysis here!

    1) By making assumptions about the significant digits of the variables, you can calculate what the maximum and minimum of what the measurements could have been interpreting.

    2) the standard deviation is , p = sqrt (sum { [ (partial derivative wrt variable)(error in variable due to significant digit)]^2 }

    that is to say, the variance is equal to the squares of the partial derivatives multiplied by their respective possible errors.

    3) how much do these intervals overlap?

    It's not exact, but it does give you things to compare meaningfully.  This is what we do for reports in my engineering physics classes.

  6. Unit Labeling problem. 27.2 PSI and 25.3 PSI should have been labeled PSIA. PSIA=PSI Absolute. Sal said it, but didn't write it that way. In conditions were there may be confusion – sometimes to make things clear engineers/scientists label pressures PSIA or PSIG. PSIG=PSI on a Gauge.

  7. While the video is highly scientific and logical, I would just like to add that the balls were probably measured in doors. In other words, by the time the refs were measuring them, the temperature that was applicable is no longer 50 degrees, as those balls were not measured outside, but from inside. So, the real temperature change were minimal.

  8. Thank you for the explanation. Been linking for someone to run the math on this. One question though. Why were all the colts footballs properly inflated and 1 of the patriot footballs? Would this effect all the footballs on the field equally?

  9. Why not just use N/m^2 or Pa for pressure? I never heard of PSI.
    It doesnt change the answer, but Pa is more universal.

  10. Great explanation except you still have to fudge the final numbers a little to get the true result. The real issue is out of hundreds of thousands of games of football how come this pressure drop has only occurred significantly once? Should not the league be aware of this occurring time and time again if it is just a fact of nature?

  11. Well…the question becomes, were they inflated indoors?
    What if they were inflated outdoors? The Patriots still aren't off the hook.

    And this cannot be the first time this has happened (IF the footballs were inflated indoors). It's still suspicious that the players and refs did not notice a 2 pound difference in the footballs.

  12. The NFL footballs are lot more technically created so that that factor doesn't affect them as your video claims it doesn't otherwise all the footballs would have that problem not all but one and the Colt's footballs would of had the same problem.

  13. What effect would water vapor in the ball condensing to liquid have on the pressure change? This video is applying the ideal gas law, but our ordinary air is not an ideal gas, and condensation can lead to far larger changes in pressure than those predicted under the ideal gas law, such as those that happen in a steam engine.

  14. So, just measure the pressure in the ball, outside, when temperature has had time to stabilize, before the ball is put into play.  Both teams use the same ball.  No calculation is then necessary.

  15. "NFL head of officiating Dean Blandino confirmed today that the NFL didn’t log the exact PSI of each football." http://profootballtalk.nbcsports.com/2015/01/29/nfl-didnt-log-the-psi-of-each-patriots-football/
    "Report: Under-inflated balls were approved by refs prior to AFC Championship game"
    http://q13fox.com/2015/01/27/report-under-inflated-balls-were-approved-by-refs-prior-to-afc-championship-game/
    And, shouldn't the balls have gone back to their "original" inflated state once taken back inside!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  16. Great analysis Khan.  You just left out one problem, or 12.  Everyone keeps bringing up 11 out of 12 footballs were under-inflated but the true statement is that 13 out of 24 footballs did not reflect the 2 psi drop and the remaining 11 that did were all under New Englands control.

    An explanation that only works 11 out of 24 times does not hold up.

  17. Very educational, great video, but why were the Colts balls all correct and why were 11 of the 12 under the PSI? Seems like all 24 would be affected similarly.

  18. The Science behind the play….. ¬† ¬†Now tell me Jamie…. ¬† are they taking this "game" a little too far ? ¬†LOL…. ¬†¬†

  19. What was the % gained in ability to catch the ball? Assuming the difference is negligible the closer the ball is to the target receiver (if it hits you in the chest you were going to catch it anyway) wouldn't this increase the % of passes being intercepted? And turnovers are a much larger factor in the game as opposed to first downs or receptions. 

  20. Based on these calculations we would need an initial tempurature of 85 – 90 to reach the same percent differential.

  21. there are several games a year played in cold weather and NEVER before has this been an issue (Deflation due to temp change). I would think my 10 second observation would be easier than 9 minutes of math and have the same conclusion

  22. Bullshit. This analysis presumes the footballs were measured outside in the weather. They were not. 

    The pressure of the footballs was measured in the referee's locker room both times, as the rules require.  They had a little time to "warm up" at half time.  The balls were dry and at approximately the same temperature as when first measured, perhaps a little less, but all of the footballs were measured . . .Colt's & Patriot's.  

    The Colt's footballs were still at approximately the same pressure as when first measured. The Patriots footballs were significantly less.  Only one Patriot football was OK.  That one football was NOT a kickers ball, as some suggest.  Kicker's footballs are prominently marked by rule to ensure they cannot be accidentally mistaken for a regular game ball.  So they missed one.

    The more relevant evidence is statistical, not scientific.  Look how rare fumbles by the Patriots became compared to all other teams just as soon as Brady convinced the NFL to allow the teams to prepare their own footballs.   It was a very bad idea.  Even players who had average fumble rates suddenly had very few when traded to the Patriots.  Make every football the same for both teams and put control in the hands of the officials, NOT the teams, just like the kicker's footballs.  A deflated football is considerably less likely to be fumbled.

    The rule change Brady promoted was stupid and poorly thought out.  It's too late to do anything about the past.  The eight or nine year advantage the Patriots had should be ended by changing the rules back to the way they were before.  The teams should all use the same footballs at the same pressure, just like the kicker's footballs.

  23. the NFL should gauge all the game balls for every game next season, in exactly the same way they did for the NE/Colts game, and record temperatures and pressures and see if there is any actual difference, since too many variables are at play here.

  24. thanks for the explanation

    According to the wells report the Patriot balls actually deflated from 12.5 PSI to 11.3 PSI. So your explanation explains it. If the Wilson gauge was used to measure the games before the game and at halftime, only 3 Balls had lower PSI than 11.4 PSI

  25. Thanks Khan very much for applying science to do the preliminary analysis on this issue. 
    There is, however, a strong circumstantial evidence for purposely deflating the football (copied and pasted from Wikipedia): 
    In several texts between Jastremski and McNally, the two mention and joke about inflation, deflation, needles, and gifts from Tom Brady to McNally. Tom Brady was a constant reference point in these discussions. McNally referred to himself as "the deflator" in a text message to Jastremski as far back as May 2014.[21]:75

    Scientific analysis was performed by Exponent and supported by Dr. Daniel Marlow, a professor of Physics at Princeton University. This analysis concluded that within the range of game conditions and circumstances studied, no set of environmental or physical factors could account for the loss of air pressure exhibited by the Patriots game balls. The scientific study supported the report's conclusion that the loss of air pressure may be accounted for by human intervention.[21]:130‚Äď31

    As for why people do this:
    Underinflating a football may make it easier to grip, throw, and catch, and may inhibit fumbling, especially in cold rainy conditions.[5]
    The official rules of the National Football League require footballs to be inflated to a gauge pressurebetween 12.5 and 13.5 pounds per square inch (psi) or 86 to 93 kPa. The rules do not specify the temperature at which such measurement is to be made.[3]In 2006, the rules were altered so that each team uses its own footballs while on offense. Teams rarely handle a football used by the other team except after recovering a fumble or interception.

  26. To try and answer why Colts balls were not deflated as much as NE's…it is possible that Indy's Luck likes his balls inflated higher than 12.5.¬† It is also entirely possible, that the Pats KNEW about the Ideal Gas Law, or that there would be some natural deflation.

    And to also comment on something we all remember from our childhood:  Ever play with a basketball you left in your driveway in the summer sun.  That thing was so inflated it would bounce 5 feet high.  I remember bringing that ball inside, and it took an HOUR to get back to normal.  I truly have to buy the science more than the foul play notion.

  27. According to the Wells Report the average reading was 11.3 psi. That's a drop of only 1.2 psi. 1.2/27.2=4.4%. So based on that, the footballs started out even higher than 12.5 psi.

  28. You are assuming that the volume of the football does not change with pressure? Why would you do that? Do you not believe that a football is softer at lower pressures than at higher pressures?

    To properly test this analysis, you would need to account for any change in the volume of the football in the calculations – lke by submerging both examples in water and measuring their displacement.

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