“I was just wondering how much iced tea it would take to cover the state of Texas if it were poured out in puddle a single molecule thick.”

So one day Erin and I are driving down the road and she asks, “So, what are you thinking?”  Well, that was the answer.

Yes, this actually happened.  Erin likes to share this discussion, too.  When she does, people look at me a little differently.  I don’t think that’s a good thing.

However, it’s become such a topic of discussion, I am now compelled to actually do the calculation.

The answer wasn’t too hard to derive…so let’s get to it!

First, we need to know how big Texas is – approximately 268,581 square miles (according to Wikipedia).
Next, we need to be a little clearer about what we are calculating.  If we “pour out iced tea” – well, how thick of a layer would that be?  After all, we can’t calculate how many gallons (a volume) without knowing the length and width (area) and height (or depth).  One of my wise guys friends asked about the tea absorbing into the ground.  Why stop there?  I mean, we probably have to deal with evaporation and buildings and sewages systems…  As you can tell, the answer can get quite absurd if we don’t just draw lines somewhere.
Let’s shoot for a depth of one inch.
tea_equation
The answer is a REALLY big number: 4.7 trillion gallons!  Okay…that’s crazy.  Federal deficit crazy.
So, I started thinking about the other “extreme” – what if the layer of tea was just one molecule thick?  Try Googling “how thick is tea.”  Absurd.  Since tea is mostly water, I just assumed the average “thickness” of a water molecule and I didn’t really worrry about molecule packing or anything.  Reworking the math a little (instead of multiplying by 1 inch, we multiply by 2.7 Angstroms) and we get roughly 51,000 gallons.
Yes…that’s much better.  Of course, at one molecule thick, that would probably evaporate before it even hit the ground.