## Tuesday, January 6, 2015

### Wind and fire

In many ancient traditions, the world is made up of a small number of elements, including water, earth, fire, and air.  But since I'm more of a gamer than a classicist, I see the classical elements as a motif that gets way overused in fantasy video games.  You know, you have your fire spells, which engulf things in flame, and your wind spells which create miniature hurricanes, and so on.

The classical elements are clearly a timeless idea.  But the thing is, we know that the underlying mechanism between wind and fire are pretty similar.  Both air pressure and air temperature arise from random motion of molecules in a gas.  Why, then, is there such an obvious distinction between getting burnt and getting blown away?

This question was asked by a reader.  I also wrote something about temperature and pressure back in 2010, which was a bit more technical.

Defining terms

Temperature is basically "the willingness to transfer energy".  That is to say, a hot object will transfer heat (energy) to a cold object, and not vice versa.  The exact rate of transfer is influenced by many factors, but temperatures control the direction of transfer.

Temperature is distinct from thermal energy, which is the amount of energy in the random small-scale motion of a material.  In general you can have objects with more thermal energy but lower temperature.  For example, a cold glass of water has more thermal energy than a lit match, simply because it's bigger.  But this can be true of equally-size objects, since it depends on the object's microscopic properties.

Pressure is the force that a gas applies outwards.  Analogous to the above definition of temperature, pressure is "the willingness to expand".  The pressures we are used to are incredibly strong.  At sea level, the pressure is 2,116 pounds per square foot.  The reason this force does not push you left and right is that usually the forces from air pressure cancel out exactly in all directions.

We often talk about pressure applying force on surfaces, such as the walls, floor, and ceilings of a room.  But the gas also applies force on itself.  You can divide a room of gas into a bunch of small units, and each unit of volume applies force on the adjacent units of volume.  All the forces cancel out except at the surfaces--the walls, floor, and ceiling.

A room is divided into many units of volume, and the red arrows show the forces applied outwards by each volume of air.  The image is mine.

Wind is actually distinct from air pressure.  Wind is the large-scale flow of gas, a velocity averaged over all the molecules that make up the gas.  Wind is often caused by gradients of air pressure.  For example, if there are two nearby regions, one with higher pressure than the other, then the pressure gradient will push air from the high pressure to low pressure.

It seems pretty intuitive that when wind is flowing a certain direction, it will push you in that direction.  But the physics behind this is actually horribly complicated.  When the air flows around you, it creates a slight pressure difference between one side of you and the other side, and that pushes you in the direction that the wind is going.  The details are beyond the scope of this post.  Just know that it's correct to say that when you're blown away by wind, it's caused by air pressure, but that wind and air pressure are not the same thing.

Random motion of molecules

Image from Wikipedia.  Depicts randomly moving particles in a box, applying force to the walls of the box whenever they collide.

Microscopically speaking, the source of air pressure comes from collisions of molecules.  All the molecules of a gas are moving around randomly, and when they collide with any surface they apply some force for a brief instant as they bounce backwards.  Averaged over many molecules, the pressure can be considered to be constant over time.

At room temperature, the mean speed of air molecules is about 1800 km/hr.  For comparison, this is about as fast as the fastest winds on Saturn.  A hurricane with winds over 252 km/hr counts as category five.  The speed of sound is about 1,200 km/hr.  So there's a big difference between wind, the average velocity of molecules; and pressure, which comes from the random motion of molecules.

As it turns out, in a gas, the temperature--the willingness to transfer heat--is also related to the random motion of molecules.  This makes sense, since the faster the molecules move, the more "willing" they are to give up some of that energy to whatever they collide into.  Furthermore, the pressure and temperature of a gas are proportional.  It doesn't even matter whether the molecules are big or small, although it does depend on the density of molecules.

Why won't a fire blow you away?

There are basically two explanation which play roles.

First, the temperature and pressure may be proportional in a gas, but that doesn't mean that the rate of heat transfer is proportional to pressure.  Direct collisions is one mechanism of transferring heat from a gas to a surface, but radiation is another important mechanism.

In more detail: Radiation is the transfer of heat through light.  For example, light can be created whenever two molecules in the gas collide with each other.  This bit of light can travel to a solid and get absorbed as energy.  Light also carries a little bit of momentum, but it's not enough to cause significant pressure in this situation.  Where did the momentum go?  Absent any wind, the average momentum of the gas is zero to begin with, so the momentum doesn't need to go anywhere.

The second explanation is that the density of gas molecules in a fire will simply decrease until its pressure is nearly at equilibrium with everything else.  Pressure is only proportional to temperature when the density of molecules is constant.

In more detail: When you create a fire, it does create an increase in pressure.  But the pressure quickly comes to an equilibrium with the surrounding, depending on the size and suddenness of the fire.  Big wildfires can certainly create big winds.  But with a small candle, there only needs to be a slight displacement of the air, and the pressure quickly equilibriates.  So you have this hot gas with fast-moving molecules, but there are also fewer molecules.  If you touch a flame, the faster, sparser gas will apply the same pressure as normal.  But since the molecules are faster, they're more willing to give up some of their energy.

It's not so much that the air molecules apply a lot of force to your finger.  It's that they're moving really fast compared to the molecules in your finger, and so when they bounce backwards they lose some of their original speed.  That energy is absorbed by your finger, possibly burning it.  The rest is chemistry.

miller said...

Much clearer! I'm starting to understand this. Thanks!

miller said...

So, let me see if I get this...

Considering a spherical balloon, with just enough air in it to hold its shape, sitting on a table at room temperature (70F) at 1 atmosphere with everything in equilibrium. (All numbers other than yours are made up, just to get the sense of things.)

The air molecules outside the balloon are hitting the skin at ~1800 mph. They're hitting the balloon from all sides, so there's no net push in any direction. Also, the molecules in the skin of the balloon are wiggling somehow at a rate about equal to the 1800 mph, so neither the air nor the skin "want to" transfer heat to the other. Basically, nothing happens.

I set a fan to blow on the balloon. Now the air molecules are hitting the balloon on one side at 1801 mph, and there are a few more air molecules on that side, so there's a net push on the balloon away from my mouth. However, since the speed of the new air molecules are still very close to the wiggling speed of the balloon's skin's molecules, they still don't "want to" transfer much heat. So the balloon moves, but the skin doesn't melt.

I put my lighter next to the balloon. Now, not only is there radiation, but the air molecules are now moving at 18000 mph near a small area of the skin, but there are 1/10 as many there. So there's very little push; however, because those few molecules are moving so fast, they "want to" transfer a lot of heat to the patch of skin, so that piece of skin gets hot, melts, and the balloon bursts.

Am I on the right track?

miller said...

And is there a difference in the elasticity of the collisions? Pressure being elastic collisions, and heat being inelastic?

miller said...