Wednesday, October 2, 2013

Scientific Thinking

I guess we have a science theme going this week.  Yesterday we discussed why you don't like science (assuming you don't).  Today I want to talk about thinking like a scientist.

If you follow me on Twitter, you know I'm on a diet.  As part of this diet I drink a lot of water.  And I mean a lot.  Up to one gallon per day.  To facilitate this water drinking, I have a 1/2 gallon Tupperware pitcher I use.  I fill it with ice and water, I fill my glass with ice and water, then as I drink the water from the glass, I re-fill it from the pitcher.  I do this twice and between the first glass of ice water and the melting ice in the glass and pitcher, I am probably drinking about a gallon of water every day.  This helps stave of hunger and some claim it flushes toxins.  I do know I get more exercise running to the bathroom every 15 minutes or so.

So I'm sitting at my desk working on something (or goofing off) dutifully drinking my water when I hear a squeaking sound to my left where the pitcher rests on my vinyl notebook which serves as sort of a mega-coaster.  And I wonder what the heck is going on.  Why is my water pitcher squeaking.

Now if I were a non-scientific thinker, I might conclude it's haunted, it's alive, or there's a little invisible mouse on top of it.  But, using Occam's Razor, I immediately reject (even without thinking about it) any supernatural explanation.  There must be a logical, scientific explanation, I realize.

I decide the squeak could be explained by the Ideal Gas Law based on the data I empirically gathered.  Okay, I see your eyes glazing over.  So follow me on this:
  1. The pitcher is about half-full of ice-water solution at equilibrium which means the liquid is at almost exactly (because of my altitude and the water not being 100% pure) 32 degrees Fahrenheit (0 degrees Celsius).
  2. The room temperature is about 72 degrees F (22 degrees C).
  3. My water pitcher
  4. The pitcher is sealed (see picture) so the volume in the pitch is constant, therefore, between pouring out water, the volume of the ullage is constant (scientists tend to use unfamiliar words because they describe things more precisely).
Nature is always trying to reach equilibrium so the warmth of the room will be warming the ice water and the air above it (in the ullage).  As long as there's ice (which will slowly melt to compensate for the warming water) the water should stay at 32 degrees F.  But the air will warm.  This is called "thermal equilibrium."

So here's the Ideal Gas Law:


I know, gibberish.  So let's break that down.

P is the pressure
V is the volume
n is the amount of gas (measured in "moles" but don't worry about that)
R is the "Ideal Gas Constant" which means it's a number that doesn't change.
T is the temperature.

In the case of the pitcher of water, volume (V) of the ullage is a constant (between pours of water), the amount of air in the ullage (n) is a constant (again, between pours).  The gas constant is always a constant (funny that), but the temperature (T) is rising because it is probably around 32 degrees F but it wants to be 72 degrees (the temperature of the air around it) because it wants to reach thermal equilibrium.

This is, to me, the beauty of science and engineering, that something as simple as the Perfect Gas Law can describe real-world happenings.  (And if you don't think the Perfect Gas Law is simple, take a look at Bernoulli's equation!)  Basically, if V, n, and R are constants, and T goes up, then our math teacher (oh, no, not math!) taught us that P has to go up.  Or to use algebra:

And that can be simplified as:
(Because everything but T and P are constants, I just wrapped them up in one constant I called "K" and if you care:
Clear as mud?)
So from P=KT, if T goes up, P must go up.  So what is happening in my water pitcher is that the temperature of the air in the ullage is rising so the pressure is increasing but the seal at the top is not perfect and the higher-pressure air, again, due to nature's preference for equilibrium (this time of pressure), is trying to escape to the lower-pressure region outside the pitcher, and a little is getting past the hole cover, and it's squeaking as it escapes. Quod erat demonstrandum.
And yes, that was a long ways around to "the air is warming up, increasing in temperature, and trying to escape."  But, math and science can be used to explain the phenomena and that works for so many things in the world.  The math gets tough (believe me, I took Chemical Engineering classes) but it's the same principle.  You think like a scientist and describe the world around you in terms that can be modeled mathematically.
So next time you're faced with a mystery, approach it scientifically.  Maybe then you won't believe in ghosts.

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