February 28, 2015

## When Does Pee Freeze in Mid-Air?

Category: Parenting

It all started when iCaspar wrote a post on this and I just had to ask what his response was mainly out of curiosity to such a brilliant question posed by his kid.

He then followed up with a post and explained it all with physics and Newton’s law of cooling:

Pee is mostly just water with a little urea, a trace of salt and even smaller traces of other stuff. Both urea and salt cause the freezing point of water to be depressed. Since most of the 5% of pee that’s not water is urea, let’s assume (hey, I’m was a physics major, we make assumptions. You’ve heard the one about the square chicken, right?) the urea concentration is a little less than 4%. Or, better yet, since we can find an actual experimental result for it here, let’s say a molar concentration (formular weight of solute per 1000 grams of solution) of 3.389. At that concentration, the freezing point compared to pure water is depressed by 5.594°C.

So the ordinary freezing point of pee is around -5.6°C (21ºF).

This makes sense. If you put pee in your freezer next to the bottle of vodka (I’m not recommending that you actually try this at home, just that you could) it freezes way before your vodka does.

21º isn’t all that cold of course, but to freeze in mid-air, it would have to be a lot colder. For one thing, your body temperature is 98.6°F (37°C), which means your pee needs to cool by 76.6ºF (42.6ºC) in a very short time.

Let’s assume that you’re out with your Boy Scout troop at winter camp. Let’s say you and your friends decide to try mid-air pee freezing and you can manage to pee upward high enough to give your pee a generous 1.5 seconds from “exit” to ground. The cooling rate would need to be 28.4ºC/sec.

Newton’s Law of cooling tells us that:

$T(t) = Ts + (To - Ts)*e^{(-k*t)}$

Now, Newton’s very logical law of cooling went right over my head, but iCaspar’s detailed and very animated explanation made it all very interesting to read further. I thought he did a brilliant job explaining physics in a very human term.

The final answer to if and when pee freezes in mid-air? Well, you gotta head over to his blog and read all about it here.

It would be interesting to try to explain it to Squirt when he gets to that age if we ever move to a freakishly cold country. Who would have thought a question on freezing pee would be so interesting!