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?

Comments

  1. #1 Evan Berkowitz
    August 17, 2010

    Another fun bonus question: why don’t we hear sonic booms all the time from every air molecule going faster than sound?

  2. #2 CCPhysicist
    August 17, 2010

    Two observations:

    1) As you noted, but didn’t quite say, temperature is the average energy in the REST FRAME of the substance, the energy you have when the macroscopic KE is zero. There is a very good analogy between this internal energy, other internal energies (such as those associated with latent “heat”), and the mass energy you have even when an object is at rest.

    2) The other missing word is convection. The three ways you can lose heat are by conduction, convection, and radiation. Wind provides driven convection, removing that boundary layer of hot air (produced by conduction and radiation losses) more effectively than simply “warm air rises”.

  3. #3 asad
    August 17, 2010

    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

    Ah, but even wind on a 100 degree day will make you feel cooler, even though you’re being hit by air that’s warmer than your body temperature. The reason, of course, is because we sweat, and the moving air facilitates evaporation of sweat which removes a considerable amount of energy from the surface of our bodies.

  4. #4 BaldApe
    August 17, 2010

    Another question would be, How far does an average molecule go at that speed before colliding with another one?

    ISTM that there is a world of difference between molecules going a tiny fraction of a meter vs. molecules going hundreds of meters at that speed. Like the difference between a box of marbles vibrating, and a similar mass of marbles thrown at the same speed.

  5. #5 Ethan Siegel
    August 17, 2010

    Asad,

    That’s not true. Wind, when the air is hotter than your body temperature, *feels* hot to your skin.

    The net result to your overall body temperature may be a cooling effect due to the evaporation you describe, but the thermal receptors on your skin — the things that feel heat — will make you feel hotter, rather than cooler.

    I’ve lived in places where that is the case, and it sucks for exactly that reason.

  6. #6 beebeeo
    August 17, 2010

    why isn’t the speed of sound more like 500 m/s than 300 m/s

    I am not a physicist but I guess its because when one air particle hits the next one, they are unlikely to be moving on exactly the same direction as the sound wave, both before and after the collision. Because the particles move in all directions, only the velocity that is parallel to the sound wave counts. Is that correct?

  7. #7 Eric Lund
    August 17, 2010

    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?

    Sound speed refers to a collective motion, not a random motion, so degrees of freedom enter into the computation. That’s why the sound speed formula has a γ (the ratio of specific heats; it’s 5/3 for monatomic gases and around 7/5 for diatomic gases at a temperature such that the rotational modes but not the vibrational mode are thermally excited, as is true for temperatures generally found near Earth’s surface) where the thermal speed has a 2: some of the energy of the sound wave goes into random translational and (for diatomic and polyatomic molecules) rotational motion of the particles. So Beebeeo @6 was on the right track.

  8. #8 Benjamin Geiger
    August 17, 2010

    asad/Ethan:

    That also depends on the humidity. 100F air at near 100% humidity will make you hotter, no matter how much you sweat. Your sweat simply can’t evaporate fast enough to reduce your temperature noticeably.

    But yes, even when the humidity is low enough to allow sweat to work, blown hot air doesn’t feel significantly cooler than still hot air.

    (I live in Florida, and have traveled to places like Palm Springs, CA.)

  9. #9 Mu
    August 17, 2010

    At 100 F and 100% humidity you don’t evaporate anything, unless you’re running a pretty good fever.
    I always thought the temperature definition via molecular speed is neat, but it fails badly under vacuum conditions. You get extremely fast moving molecules in the outer atmosphere, nevertheless you’d freeze to death due to there not being all that many of them, radiative heat transfer beating convective by a mile under those conditions.

  10. #10 Jim Thomerson
    August 17, 2010

    When I was living in New Orleans, I visited home in the Texas Hill Country during the summer. After lunch I lay down on the cot out on the back porch. There was nice breeze blowing, and I thought, “How comfortable it is out here.” Then I looked at the thermometer on the wall in the shade. It registered 108 degrees F. A dry heat, don’t you know. In hot and dry, you want to be completely clothed so the hot wind evaporates sweat out of your clothes and makes them feel cool.

  11. #11 Del Cotter
    August 17, 2010

    A fun question I like is: how hot is a rocket exhaust in space? Assume a very efficient rocket that makes the best use of the hot gas coming out of the combustion chamber.

    If it’s hot, then doesn’t that contradict the efficiency assumption above? And if it isn’t hot, then why do things that get in the way of the exhaust get hot?

  12. #12 Eric Lund
    August 18, 2010

    I always thought the temperature definition via molecular speed is neat, but it fails badly under vacuum conditions.

    That definition of temperature is the correct generalization to vacuum conditions. It works as long as there are enough particles around to do thermodynamics. You can even extend the generalization to collisionless systems where the particle distribution isn’t Gaussian (e.g., the solar wind is often observed to have a power law tail). What fails is your intuition of temperature–yes, you will freeze in the Earth’s shadow, even when the ambient plasma has temperatures in excess of 10 MK. The reason this is not a violation of the Second Law of Thermodynamics is because you are radiating to the effectively infinite heat sink of deep space at a much faster rate than the ambient 10 MK plasma can transfer heat to your body.

    Assume a very efficient rocket that makes the best use of the hot gas coming out of the combustion chamber.

    The temperature of the exhaust is irrelevant in space because the dominant effect is due to a dense gas expanding into a vacuum. So you shape the nozzle to aim the resulting flow in the desired direction, and that flow ends up dominating over thermal motion.

  13. #13 Tom
    August 18, 2010

    One thing glossed over in the earlier exchange is that your body doesn’t merely sense temperature; it also senses heat exchange: a piece of metal feels colder than a piece of wood at the same temperature, owing to the higher thermal conductivity of the former. While asad’s specific example may be suspect, it is true at lower temperatures because you are losing energy, even though the surface temperature may not be dropping very much. Which of course is the whole idea behind the wind chill factor.