Kinetic Theory of Sweat - Part Deux

It is supposed to top 100 degrees today, which has me thinking about sweat.  And I’m sure it makes people curious about how it is that sweating cools us off.  You ARE super curious about that, right?   

As a recovering engineer (and a major Cliff Claven fan), I know you are curious, and I am here to satisfy your curiosity.  Rather than delve deeply into textbook explanations, let’s try a familiar sports metaphor.  

First of all, it isn’t the process of sweating that cools us off; we cool off when that sweat evaporates, and leaves our bodies, taking heat with it.  If it can’t evaporate, we don’t cool off.

(Brief technical bit - I promise it will be brief) Heat is a measure of the average kinetic energy of all the molecules in whatever is being measured.  The hotter something is, the faster the average motion of its molecules (and thus, kinetic energy) .  The key word here is AVERAGE.  There are billions of molecules of water in a bead of sweat, some moving fast, and some less so.  The temperature we sense is the average.  

Evaporation is when some of the fastest molecules actually move fast enough, they leave the puddle of sweat.  Because they are the fastest, when they leave, the AVERAGE speed of the ones that stay behind is lower, which, by definition means it is cooler.  This is exactly how those evaporative swamp coolers work … the ones that use a fan to blow hot air over a water.  

For those who have been missing professional baseball this summer, here’s a way of looking at it.  Suppose your home town has a minor league baseball team - a farm club connected with a major league team.  Think of kinetic energy as the skills of each player on the team.  As they train and develop, their skills improve … they get hot, and start winning.  The major league team who owns the club starts to pay attention - especially to the hottest players on the team - and one day, that player gets called up to ‘the show’.  Without this player, the AVERAGE talent of the team decreases … they aren’t quite as hot.  That player’s phase change from AAA to the majors sucks up a lot of heat from the team.  Maybe the coaching staff focuses more on the remaining players, and they get hot again … and the big leagues come and snag the next hottest player, and the team cools off again.  

This metaphor works as long as there is somewhere for the best players to go … as long as the majors have room to take them.  If the team is insulated, it remains hot.  

I’ll stretch the metaphor just a bit (and hope it still works), to see if we can address why sweating doesn’t help when it’s humid.  Let's say that the major league team calls up your best player, then sends down one, whose skills have cooled off a bit (by big-league standards).  The cooling of minor league team is now offset by the addition of this new player.  A minor league team operating in an environment where there is a surplus of highly-talented players in the majors can’t really cool off by sending up their hottest players, if they are just going to be replaced immediately with one who is just as hot.  

That’s all I’ve got for now.  Time to go out to the kiddie pool (would that be like Little League?)!  



I gave this whole thing a shot a few years ago.  Not sure if my current explanation is any better than my attempt was then:
https://askdoctorwizard.blogspot.com/2013/09/the-kinetic-theory-of-sweat.html

The Sinusoids of Fall

This time of year, it's not unusual to get the sense that the days are becoming shorter very quickly.  

This is not just an illusion, it is actually happening.  As we make our way from long summer days to the long nights of winter, the day-to-day reduction in day length is never greater than it is near the autumnal equinox - and conversely, the day-to-day increase is never greater than the first day of spring - the vernal equinox.  

This is an excellent illustration of what scientists call a sinusoidal function; a function whose form looks like an unending series of waves (technically, 'sine waves').  

Sinusoidal functions are are all over the damn place in nature and science - from the pendulum on a grandfather clock, the vertical motion of an engine's piston as the crankshaft turns, or the up-and-down motion of a weight hanging at the end of a spring.  

This is a graph of a simple sine wave.  Notice that when the wave is at the top and bottom of its path, it is just about level.  This could represent the summer and winter solstices.  The days are at their longest, and shortest, respectively, and hardly change at all from day to day.  Then the slope gradually increases, until it is steepest when the curve is exactly at zero (equal lengths day and night).  From there, the slope gradually becomes less steep, until it reaches the other extreme, at the top or bottom, at which time, the process begins in reverse.  

We may sense the stability of the solstices; as the enjoying the long days of early summer, or the interminable wait in December and January, waiting for the longer days of spring.  In both cases, things are not changing very rapidly.  

If this hasn't bored you to tears yet, consider this further illustration.  

The animation below dynamically illustrates the relationship between day length and the rate of change in day length, using two related sine waves.  Think of the sine wave along the bottom of the graphic as day length, and the vertical wave on the left as the rate of change in day length (what calculus nerds call the first derivative).  It is when the day length is at the middle that the change is at its maximum.  

I could go on, but that would surely induce a nap, if I haven't already.