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:
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:
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…