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. 

Fridge Thermodynamics

Alright, engineer cadets, and appliance-repair apprentice wannabees, I have a story problem for you.  

Imagine a hypothetical beer fridge.  Like many beer fridges, it is kept in the garage – though in the yard, at the end of an extension cord, next to the car up on blocks would work as well for this example … but I digress.  

So, in addition to beer, there is ice cream in the freezer.  Everything works fine, even in the heat of summer (the one in the yard is under s shade tree).  

But a strange thing happens when it gets chilly outside.  It’s all good until it gets down to about 40°F.  At that point, the refrigerator continues to work just fine, but the ice cream in the freezer softens up a little.  Then, when it gets to the mid-30s, everything in the freezer slowly melts.  When it gets below freezing, it hardens back up, but then softens up again between 33°F and a bit over 40°F.  When the weather gets warm again, it freezes up again just fine (though thawed and refrozen ice cream is never really the same again.  

Gravity Critique

Lost of people loved the movie Gravity.  I am not one of them. I get it ... big-name stars, and pretty special effects.  But if you're going to name your movie after a physical phenomenon, it somewhat behooves you to get that phenomenon right.

And they don't.  'Gravity' totally distorts gravity.  One of the key tension element in the movie is a marauding pile of space junk, left over from an explosion, that whips by every ninety minutes, threatening to kill the stranded astronauts.  From a cinematic perspective, I get it that you need tension - but this would not happen.  Here's why:

The orbit (direction, and altitude) of a spaceship , or anything else in orbit is the geometric sum of two components (vectors);

• Gravity, is causing it fall toward the Earth
• Inertia, that drives it forward in it’s current direction

In a stable orbit, the vectors sum to the shape of the orbit.  This can be visualized as a rectangle, with one side as the thrust vector, the other side as the gravity vector, and the diagonal as the actual direction (vector sum). 

The spaceship cannot control the magnitude of  the gravity vector, but blasting the engines increases the inertia vector. 
Accelerating, changes the relative effects of inertia and gravity, increasing the length of the rectangle, relative to the width … in effect raising the craft to a higher orbit (bigger circle, less curvature)

If two spacecraft had been orbiting side by side, then one accelerates, and moves to a higher orbit. 
Because the rate of falling (gravity) is less, relative to the inertia,the time required for each orbit is longer, and (counterintuitively),from the perspective of the other craft, the faster craft will appear to fall behind.  Taken to the extreme, if one of the craft accelerated enough, it would rise to the same orbit as the moon, and only circle the Earth once every 28 days. 

Unless something happens to slow the green spacecraft, it will remain at this higher orbit, well out of the way of the slower craft.  

The movie ‘Gravity’ gets this all wrong. 

In order to add tension, the story has a mass of space junk
whipping around every ninety minutes, and slamming into
the stranded astronauts (Presumably, the director chose a
ninety-minute cycle time because we baby boomers vaguely
remember that each of John Glenn’s orbits took about
ninety minutes). 

This would not happen.  If a nearby spaceship explodes,
and one is fortunate to avoid the initial blast, the danger is past. 
Whatever detritus blows off in the same direction as the orbit
will accelerate, and move to a higher orbit, where it will not
be a problem.  Anything that blows off in the opposite direction
from its orbit will descend to a lower orbit, consistent with its
net post-explosion velocity. And, anything that blows out sideways,
just goes off its own way.  

The only way these every-ninety-minute collisions could occur
would be if a giant scaffolding were erected to hold the stranded
astronauts in place, in the path of the space junk. 
And this scaffolding would have to be moved about 1,000 miles
east every hour to compensate for the rotation of the Earth
around its axis.  

Pluto

Recognizing with a bit of sadness the tenth anniversary of the demotion of Pluto from planet to ‘dwarf’ planet. 

Thanks, Neil deGrasse Tyson! 

Hardly seems fair; Pluto was just discovered in 1930, and the little fella didn’t even get one full lap as a planet before the naysayers got him. Of course, that would have taken until 2178, but what's the damn hurry?

Spring has Sprung

This March, Americans are of two minds regarding the change of seasons. There are those on the east coast and Midwest for whom this offers hope of the end of one of the most severe winters in history.  Here in the Pacific Northwest, the longer days and higher temperatures confirm what we have long feared – that this will be a year with no winter at all.  

But what exactly is it that’s causing these competing feelings of disappointment and optimism?  What does science have to say on the subject?  

Thanks for asking!

The answer lies in the intersection of biology and physics.  Humans are generally diurnal; we tend to be active during daylight hours and asleep at night.  Though we don’t hibernate (at least most of us don’t), our processes tend to slow down when the days become shorter, then pick up as day length increases.  As the days (okay … the daylight portion of the 24-hour day) lengthen, we begin the transition from our wintertime to summertime selves.  

It’s not so much the length of the days that causes this, but the day-over-day INCREASE in daylight hours that affects our moods.  And there is not time when this is more pronounced than the first day of spring – the vernal equinox.  This is where physics comes in.  

You probably recall from high school science that the seasons are caused by the tilt of the Earth’s axis, relative to our orbit around the Sun.  If you look at a chart of daytime versus nighttime throughout the year, the result becomes clear.  The graph is a classic sinusoidal function – like a radio or sound wave.  And one thing that’s fundamental to these functions is that, as the function reaches its neutral position (the spring and autumn equinoxes), the rate of change (the ‘first derivative’ in Calculus terms) hits is greatest.  

This effect applies everywhere except at the equator, where day time and nighttime hardly vary throughout the year.  At the other end, the Polar Regions go from nearly constant darkness in mid-winter to round-the-clock daylight in late June.   Scientifically speaking, the further from the equator one is, the greater the amplitude of the sinusoidal function.  
If that hasn’t adequately stolen the magic of the season from you, stay tuned. 

Next time we’ll cover how it’s the wind ABOVE one’s wings that provides the lift; so if a friend says you’re ‘the wind beneath my wings’, you’re actually being told you’re a drag.  Future lessons will cover how it’s generally darkest a really really long time before the dawn (around midnight).  

If this all seems a little much, there is an alternate explanation.  The Earth is coming to life in joyous celebration of Persephone’s annual release from captivity in the underworld.  

You’re welcome!  

Chain Reactions and Immunization

I remember learning about nuclear chain reactions when I was a kid. 

Basically, certain isotopes of Uranium (U-235, for example) are unstable, and if they’re hit by a neutron from another unstable U235 nucleus, it very rapidly decays into two smaller atoms, emitting more neutrons into its environment, and generating heat in the process. 

If there are no other vulnerable atoms in the vicinity, the neutrons just fly harmlessly off into space.  But if one of these neutrons impacts another U235 nucleus, it will also split, emitting even more reactive neutrons, and more energy.  If the concentration of U235 atoms is high enough, this reaction will sustain itself, generating heat to boil water, run a turbine and produce electrical power.  If it’s even higher … you get a nuclear bomb. 

To illustrate the concept, think of a place where people gather – Disneyland for example.  Say one kid with the measles shows up and sneezes, or wipes his nose, then touches a handrail.  If all the people around him are vaccinated, this is a non-event – except for that one kid.  But if the virus ejected in his sneeze comes into contact with an unvaccinated kid, he gets sick, too.  Then when he sneezes, the pattern is repeated.  If enough kids are not vaccinated, the result is an epidemic. 

Since the late 1950s, a range of vaccinations has been the norm for most people.  As a result, few people have been exposed to measles, or a number of other contagious, preventable diseases.  This lack of exposure has led to complacency, and a sense that vaccinations are really optional.  There is even a mythology—unfounded by empirical science—that vaccines are dangerous.   Vaccination for any individual is optional, and safe – as long as everybody else is vaccinated; because the individual is never exposed.  But there is now a concentration of non-vaccinated people within our population to create and sustain epidemics. 

At the concentration we’ve reached, widespread complacency puts us all at risk of a chain reaction of infection.  Many of these diseases are highly contagious, and we are all vulnerable – even if we exercise regularly, eat a diet high in omega-3 fatty acids, and—sad to say—even if we vote Democratic. 

Seriously … get vaccinated, and get your kids vaccinated.