Last week I wrote that the kid had asked me how cold it has to be before your pee freezes in mid-air.
There’s an ongoing legend (you can’t call it an urban legend here because it’s just not urban, not by a long shot) in these and many parts of the northern US that if it’s cold enough your pee will freeze before it hits the ground. I think it’s perpetuated mostly by the Boy Scouts who want to impress their friends after their winter camping trips.
Anne asked what I gave the kid for an answer. For the record I told him, “I’m not sure of the exact freezing temperature of pee.” But what if there were a way to really know the answer to the kid’s question? This may be a question better left to the brilliant Faraday sisters, I’m going to take a shot at it.
For starters, let’s consider the ordinary freezing point of pee. Freezing point depends on the chemical makeup of a liquid, which, in the case of pee, can vary from one person to the next. It so happens that when they were sending astronauts into space for the moon missions, NASA commissioned a detailed study on pee back in 1971.
I’m not going to presume that you’re interested in reading the whole thing, so let’s just cut right to the chase. According to the summary on Wikipedia:
Urine is an aqueous solution of greater than 95% water, with the remaining constituents, in order of decreasing concentration urea 9.3 g/L, chloride 1.87 g/L, sodium 1.17 g/L, potassium 0.750 g/L, creatinine 0.670 g/L and other dissolved ions, inorganic and organic compounds.
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(-kt)
t is the time in the preferred units (seconds, minutes, hours, etc.)
T(t) is the temperature of the object at time t
Ts is the surrounding constant temperature
To is the initial temperature of the object
k is a cooling constant for whatever substance is involved.
In our case, we know that:
t = 1.5 seconds,
T(t) = 22ºF,
To = 98.6ºF
We want to find Ts (the surrounding constant temperature). The problem is that we have no idea what the cooling constant k is. The cooling constant for water (or any object) varies, depending on it’s mass, surface area chemical make up, etc. So the only way to figure it out is to get an actual reading on the temperature of a stream of pee after a known time at some other known ambient temperature. Unfortunately, I’m not finding on almighty Google where anyone has reported (admitted?) actually doing that.
So, in the absence of any actual data, let’s make a few more assumptions, shall we? (Is that an unfortunate pun?)
First, let’s assume, since pee is mostly water, that we’re basically talking about freezing water.
Second, I found a report by Laura Lowe from an experiment she did as a student at the University of Georgia where she found the cooling constant for some water (we don’t know it’s volume or surface area) was 0.0293. Now, that was probably for a beaker of water sitting in a lab. A stream of pee would have much less mass and much more surface area. So, let’s say that alters the constant by a factor of about 10. So we can assume a constant for moving pee at around 0.3.
With an assumed k = 0.3, we can solve Newton’s law of cooling equation for Ts, and we get -112ºF (-80ºC).
That actually sounds about right. When we used to play around with the liquid nitrogen in the physics lab in college, we froze lots of water-based things in less than a second, but the temperature of a liquid nitrogen bath is about -320ºF. Freezing a little bit of water in a second and a half could be done without going to that kind of extreme.
Still, -112°F is colder weather than I care to go out and pee in. And it’s colder than most Boy Scouts go winter camping in. I’m not saying it’s never happened. The other day it was -110 (counting wind chill) on the top of Whiteface Mountain, 7 miles from here. But that’s counting wind chill. Maybe it happened to Ernest Shackleton when he went to the South Pole. The record low temperature there is -116.
Other than that, though, it seems as if the kid’s hopes of experiencing mid-air pee freeze are going to be disappointed.
What can I say, it’s a tough life sometimes.