I got forwarded a physics question last night asking about the connection between wind and temperature, which I’ll paraphrase as:
Temperature is related to the motion of the atoms and molecules making a substance up, with faster motion corresponding to higher temperature. So why does it feel warmer when the air is still and why does wind make you feel cold?
This is a moderately common point of confusion, so while I responded to the question in email, I’ll also appropriate it for a post topic. So, why doesn’t “windy” equal “hot,” given that wind consists of moving air molecules?
The full answer to this involves a couple of subtle issues, but I like to start with a simple-but-cool fact, which is that the speed of wind just isn’t that big a change in the speed of an air molecule.
The way to think about this is in terms of energy. Temperature is really a measurement of the average kinetic energy of a sample of particles, and the temperature is related to the kinetic energy through a number known as Boltzmann’s Constant after the German physicist Ludwig Boltzmann, who was instrumental in developing the modern view of thermal and statistical physics. Kinetic energy also depends on the speed of the particles (you may well have encountered the formula 1/2 mv2 before– v is the speed), so it’s a simple matter to relate the two, and determine the average speed of the particles in a gas at a given temperature T.
The details of the calculation are described at Hyperphysics, including a spiffy little calculator if you’re lazy and just want the answer. If you put in the mass of a nitrogen molecule (28 amu) and a slightly warm temperature (300K), you find that the rms average speed of a molecule of a nitrogen molecule in air is a bit more than 500 m/s. For reference, the speed of sound in air is around 330 m/s, so any given nitrogen molecule in the air you’re breathing is moving significantly faster than the speed of sound.
That means that wind can barely make a difference in the temperature. Hurricane-force winds have a speed of around 50 m/s, which isn’t quite 10% of the initial speed. A more typical breeze is only a few m/s which is even less noticeable.
There’s also a more subtle issue here having to do with the fact that temperature is associated with random motion, not collective motion of the whole thing. A bottle of air in a jet aircraft is not “hotter” when the plane is flying than when it’s sitting on the tarmac, just because the container is moving. The same goes for any random bit of air– if the whole mass of air is moving to the west at 3 m/s, that doesn’t change the temperature.
(I lead with the average-speed thing because I think it’s really cool that room-temperature molecules are moving faster than sound, and most people don’t know that.)
So, why does moving air make you feel cold? Well, the key is that your body temperature is almost always higher than the air around you (unless you live someplace really hot), so your body is heating the air in contact with it. On a still day, this means that the air immediately around you is at a slightly higher temperature than the air a long way away.
On a windy day, though, the air that’s in contact with your body is constantly being blown away and replaced by lower-temperature air. Which picks up some heat from your body, and then gets blown away, replaced by more low-temperature air, and so on.
This is also related to why clothes keep you warm– it’s not (just) that cloth is a lousy conductor of heat, it’s that the cloth helps trap warmer air near your skin. If you add layers of clothing, you’re keeping more warm air near you; if you remove them, you’re making it easier for warm air to leave your immediate vicinity and be replaced by cooler air.
Vaguely related fun bonus question: If the air molecules that surround us are moving at 500 m/s anyway, why isn’t the speed of sound more like 500 m/s than 300 m/s?