Built on Facts

Hot Hot Heat

Posted by Matt Springer on July 10, 2009
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From the front door of the physics building to my apartment is about two miles. That’s not all that far, so lately I’ve taken to just walking instead of riding the bus. In theory it’s a relaxing time to think and look at the interesting things that you miss from a vehicle, aside from being exercise. In practice all that’s true, but tempered by the fact that it is as hot as a freaking autoclave outside.

This entire week the temperature has peaked out at around 100 degrees, or >310 K for those of you who think in SI. It’s tolerable but not especially fun. It’ll probably get quite a bit higher on occasion this summer. But our experience of heat is subjective, and it will be interesting to tack on some numbers that are a little more detailed than just the temperature.

As with pretty much any system of particles bouncing crazily off each other, air molecules are constantly engaging in a random but statistically well-specified way. A molecule might get hit in such a way as to slow it down, only to be immediately hit again and start moving faster than originally. We’ve dealt with the Boltzmann distribution before, which tells you which fraction of the molecules happen to be at a particular speed. The higher the temperature, the more molecules will be moving faster at any given time. The equation determining the distribution is a little ugly looking, but most of it’s just scaling factors:

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

Let’s plot it for nitrogen molecules at a cool 60 degrees F (which is 288 K) and also for our blast furnace 310 K Texas weather, x axis in meters per second, y axis representing the probability density for a given molecule to have that speed:

i-7b7142f1efa09b47c3b8242f89bcb9f4-graph.png

Visually it’s not much of a difference. The hotter weather shifts the curve a bit to the right, but not by much. In fact the mean speed for the 60 F molecules is 467 m/s and the mean speed for the 100 F molecules is about 484. Like the difference in the Kelvin temperatures, it’s not all that big of a percentage change.

It feels like a large change. That’s just a mark of the relative fragility of human biological processes. We have a great deal of rather fragile internal chemistry that’s very sensitive to those slights shifts of the Boltzmann curve. Therefore some of those bodily processes are devoted to keeping our internal temperature near constant. This is difficult when the external temperature rises even slightly in absolute terms and we perceive it as unpleasant.

Sometimes it gets taken for granted, but there another thermodynamically interesting process going on in every air conditioner that’s a nice counterpoint to the thermodynamics of a sweltering summer day. Maybe I’ll save that for when it cracks 105 F…

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Comments

  1. #1 Russell
    July 10, 2009

    It has already cracked 105* here in Austin.

  2. #2 D. C. Sessions
    July 10, 2009

    If you don’t like 100F, maybe this weekend in Phoenix will seem cooler at a mere 45C.

  3. #3 Uncle Al
    July 10, 2009

    As with intelligence, it’s less the hump than the right hand tail.

    Southern California Santa Ana winds blow out from northwestern desert, over mountains to squeeze out moisture with adabatic lapse rate, then back down the other side with compression to give 110 F, 10% or less humidity, and sustained 30 mph wind. It is entirely comfortable. Evil global Greenhouse Effect water vapor is causing your evaporative misery.

    http://www.mazepath.com/uncleal/humid.htm
    There is an engineering solution

  4. #4 Eric Lund
    July 10, 2009

    Shade is your friend. Remember that whatever temperature is officially reported is the temperature in the shade (assuming you can find any); out in the sun it will be quite a bit warmer.

    Here in New Hampshire we’ve had the opposite problem: several days in a row of onshore flow keeping us under cloud cover and our temperatures locked in the 285-290 K range. The sun finally broke out today, with temperatures rising closer to the 300 K normal daily maximum. After all of that cool weather, it feels downright tropical today.

    And while I disagree with Uncle Al about 110 F being comfortable, he is quite correct that humidity makes a big difference. Inland East and Central Texas is an especially bad spot: close enough to the Gulf to get the humidity, but not always close enough to get the rain, and never close enough to get the sea breezes. Likewise, cold wet weather feels worse than cold dry weather; come winter I’ll gladly take 0F and sunny over 35F and raining.

  5. #5 Matt Springer
    July 10, 2009

    The humidity is a key point. I spent a decade of my formative years on the north shore of Louisiana’s Lake Pontchartrain, which had all the disadvantages you mention, but more so. The icing on the climatic cake was the fact that the entire region is enmeshed with millions of acres of mosquito-breeding swamp and salt marsh. They’d practically drain you dry if you weren’t careful.

  6. #6 ColonelFazackerley
    July 11, 2009

    Human core temp ~37 degrees C. skin temp around 33 (if the ambient temperature is around 20). So if the external temperature goes from 20 to 30, the temperature difference goes from 10 to 3. This is a big difference in percentage change in temperature difference. This is the salient point, as the temperature difference is what determines our body’s ability to lose the heat it makes.

    (I take the point that humidity is important too, as evaporation is a major mechanism).

  7. #7 A
    July 19, 2009

    Well, as soon as it gets colder, some nut case will give that as proof that global warming is not occurring:
    http://firedoglake.com/2009/07/18/late-night-yes-theyll-even-bs-you-about-the-weather/