If temperature is amount of kinetic energy of particles, then how can there be a cold breeze?

Question

When we put hands on A/C it gives cold winds. These winds have high kinetic energy but low temperature. How ? *don't confuse with A/C being heat pump , just an example, take antarctic blizzards. I can't understand the paradox of low temperature winds. Temperature is something defined by kinetic energy

Answer 1

The average speed of an air molecule can be approximated by the following equation, which is exact only in the case of an ideal gas:

$$\langle v \rangle = \sqrt{\frac{2RT}{M}}$$

This means at $25$°C ($298$ K) air molecules will be moving randomly at an average speed of $\simeq 467$ m/s.

Let's say that the AC cools the air at $15$°C ($288$ K) before blowing it out into the room. From the above formula, the average molecular speed will then be $\simeq 459$ m/s.

When the AC blows out the air, it does so at $0.1-0.3$ m/s (1). This means that, in the worst case, a motion of $0.3$ m/s is superimposed to an average motion which is at around $460$ m/s, more than a thousand times faster.

You can then see how the movement of the air mass as a whole is negligible: what matters is the average molecular speed in the rest frame of the air mass.

Also, even if you use a simple fan instead of the AC you will perceive the air flux hitting your skin as colder. This is known as convective cooling. See for example this post for a simple explanation.

(1) Source

Answer 2

There are two things at play here.

The Nature of Heat

Temperature, is to do with random, undirected motion. So for example, in room temperature gas, you can have individual molecules which themselves are moving at $100~\textrm{ms}^{-1}$, however on average, the velocity is zero.

When you have a body of colder air moving, it means on average their kinetic energy is lower, but they have a net "drift" velocity. That is the particles have random velocities, which corresponds to the heat, but because they've been "blown", they have an average velocity of maybe $5~\textrm{ms}^{-1}$ in one particular direction.

Why a breeze cools us down

The fact that a breeze cools us down has only a small amount to do with the temperature of the air. Consider your hand, sat in still air. Your hand will give some thermal energy to a layer of air surrounding it. (In the process of warming up that air, your hand will cool down). Now if the air is still, then that's the end of the story. However when there's a breeze, this layer of air that you've warmed up, gets carried away. It gets replaced with some new cold air, which your hand can then give heat to again, which cools your hand off again. When there's a breeze, your hand is constantly supplied with new air that it can give heat to. And so it's less that the air is a lower temperature, it's that as soon as it gets warmed up, it's replaced by a new set of cold air.

Just for fun, let's consider another similar effect. Say there's a little water on your hand. When this water evaporates, it requires heat from your hand, and so the evaporating water will cool you down. In still air, eventually the air will start to contain more water vapour, and so the evaporation process will be slower. However if we introduce a breeze, then we are bringing in fresh new dry air, so the evaporation process can occur faster, and so more heat can be taken away. This process is why if you lick your hand, and then blow on it, it cools it down.

Answer 3

The crux is that temperature is the undirected movement of particles.

Consider a very easy example of two air molecules flying with $100m/s$ away from each other, one in +$x$-direction, the other in $-x$-direction. The mean directed velocity is then $0$, however, the mean undirected velocity which corresponds to temperature is +$100m/s$.

Now suppose you accelerate both particles by $+50m/s$, so that one has a velocity of $-50m/s $ and the other $+150m/s$. The mean directed velocity is then $+50m/s$, which is the velocity of the breeze. In contrast the undirected remains at $(150+50)/2 = 100m/s$ - the temperature of the system has not changed.

Answer 4

A breeze is not "a bunch of air molecules moving in that direction". A breeze is a wave of pressure.

The speed of air molecules is on the same order as the speed of sound. They are flying around smashing into things and mostly bouncing off. You are surrounded by a barrage of minute "meteors" that are smashing into your skin and bouncing off in all directions.

Well, these meteors are mostly bouncing off each other, because at 1 atm things are so dense that the average molecule travels 68 nm before hitting another molecule.

The only thing stopping it from knocking you flying is that you are being smashed into on all sides uniformly all of the time.

A perfect vacuum is just the effect of the other side smashing into you and pushing you that way, without the support of the molecules on the vacuum side. A vacuum cleaner reduces air pressure by a tiny amount, and it causes a pretty huge force this way.

A "wind" is a relatively tiny wave of higher pressure on top of this violet stew of air molecules. We feel it because on the side it is coming from, the pressure is higher, and on the other side it is lower. Even a hurricane is a relatively small change in pressure, and is enough to pick up and destroy houses, trees, cars and people. The strongest hurricane comes from about a 10% difference in atmospheric pressure! That pressure difference from the edge to the center is enough to power the winds of that entire storm.

A 10 km/h wind is traveling at 1% of the speed of sound, which is roughly how fast air molecules move. That macroscopic motion is a tiny contribution to the average kinetic energy of the molecules of air; it has roughly 2% more KE than the same air stationary.

A 100km/h wind is now going at 10% of the speed of sound. As KE is square of velocity, at that point we are talking about 20% more KE than the same air stationary.

You'd have to approach 700 km/h for the wind to have as much KE from its macroscopic "wind" motion as it does from it's microscopic "vibration" motion.

Now, as another poster has mentioned, the velocity of air molecules is actually a touch higher than the speed of sound; sound is a wave, so it isn't going to propogate at the exact same speed as air molecules are (it will travel a bit slower). But it gives you the right order of magnitude.