a) Show that the typical speed of air molecules in the room where you're sitting is about 500 m/s.

b) Show that the typical speed is about 420 m/s at Mt. Everest. (Neglect the temperature difference between sea level and mountaintop, and assume that the air consists of only nitrogen molecules).

a)

\(\frac{3}{2}k_B T_R = \frac{1}{2}mv^2 \Rightarrow \sqrt{\left\langle v^2 \right\rangle} \approx 500 m/s\) CORRECT

b)

At Mt. Everest (9000 m) some of the kinetic energy has been transported to potential energy. A \(N_2\) molecule has mass 4.7E-26 kg, so that

\(
\Delta U = mgh = 4.7E-26 kg \cdot 9.81 m/s^2 \cdot 9000 m = 4.15E-21 J.
\)

Hence the average kinetic energy of a nitrogen molecules up there are 6.15E-21 J - 4.15E-21 J = 2.0E-21 J, and

\(2.\cdot 10^{-21} J = \frac{1}{2}mv^2 \Rightarrow \sqrt{\left\langle v^2 \right\rangle} \approx 290 m/s\) WRONG

 

I would ignore the whole potential energy thing. The pressure up there is significantly lower though.

 

I may be wrong, but I think that kT/2 is internal energy of one degree of freedom, which includes kinetic energy (velocity) of the molecule, rotation of the molecule and vibration of atoms within the molecule, and does not include potential energy in the external field, like gravity.

Thanks,
Alexei.

 

Well, I may as well get the "horrible" part out of the way. I also must make a warning that I have been banned (for life) from the Electrotecch online forum for posing such irresponsible and unpopular ideas as will be qresented here. I also must make the warning that the 2 paragraph glosses just don't suffice when discussing something as involved and convoluted as sound and sound propagation (of which molecular speed in air is an integral part).

Just about everywhere you look you get that molecular speed of air of about 500 M/s (around 1100 mph). Aftrer giving it quite a bit of thought an analysis, I've concluded that there is no "universal" speed of the air molecules at standard (or any other) temperature. In spite of the mathematical gyrations presented, the speed of the molecues must also be related to the pressure (which is also very "iffy").

The answer does not lie in plugging values into somebody's formulas or equations. The answer comes with conceptualizing the basics and building to the answer. Along the way, it's necessary (for consistency with the community at large) to assume some things and then, as you disprove them, let them fall by the wayside. It's a rather convoluted process but, I believe, well worth the effort.

I'll start with a question: If you put some air into a cylinder and compress it with a piston, where does the energy come from to make the air molecules move faster. Do the air molecules even move faster? A good case can be made that they don't.

 

If you put some air into a cylinder and compress it with a piston, where does the energy come from to make the air molecules move faster. Do the air molecules even move faster?

Betcha if you investigate the concept of "mean free path" you might find some illumination. You might also consider that doing work on the piston transfers energy to the molecules.

 

I have a real interest in this thread as I have flown a hot-air balloon for 3 years from 1998 to 2001.

The lift graphs we used depended on outside temperature, Internal temperature , barometric pressure and size of the balloon.

After burning, the pressure in a balloon balances out and you feel a downdraft of hot air as it comes out of the bottom of the balloon.
So the pressure inside is about the same as outside.What makes the lift is the density is lowered in the warmer air inside.

But the speed of the molecules increases with heat so there are more rebounds and collisions with the inside of the balloon, causing the uplift.

The previous comments suggest air molecules travel at the same speed, but a helium balloon must have much faster molecules to create lift.

I also read that hydrogen and helium molecules travel so fast , they pass out into space as gravity is not strong enough to keep them on Earth.

We are lucky our planet has strong gravity as the oxygen molecules would fly out into space if it were any less, lol

 

More about Air molecules.

The sound in your ears on a quiet night is the air molecules bouncing off your eardrums.( Unless you have tinnitus )

The noise you hear when you tune a radio between stations are air molecules hitting the ariel.

A microphone also picks up air molecule collisions if the gain is too high.

 

With the lighter gases buoyancy is more to do with the mass of the molecules than the speed.
There are actually about the same number of molecules in a litre of hydrogen as the total number of nitrogen, oxygen, etc molecules in air.
With hot air, there are less molecules per litre because it is hotter.

 

Why don't I suffocate in a tent when I zip it closed.

Most tents are waterproof but oxygen molecules are small enough to pass straight through the fabric , lucky for you.

Air molecules move so quickly that a smell is carried around a room in a few seconds . Burning toast does this as well.
House fires are deadly as the smoke gets to all parts of the room very quickly

Cigarette smoke fills a room in ther same way.

I need to calculate the speed of molecules as the temperature falls.

Is there a formula apart from Charles Law and Boyles Law.

Will a molecule slow down as it is super cooled to near -273
would it actually stop.

Any help or comments welcome

 

More about Air molecules.

The sound in your ears on a quiet night is the air molecules bouncing off your eardrums.( Unless you have tinnitus )

The noise you hear when you tune a radio between stations are air molecules hitting the ariel.

A microphone also picks up air molecule collisions if the gain is too high.

Uhhhh, no. The noise you hear with electronics is mostly the random electronic noise generated by the components themselves inside the radio, with about 10% of that being the electronic noise of the big bang. When it comes to electronics air molecules have nothing to do with it. As stated, the universe itself is full of white noise left over from creation, and the temperature is around 3°K or so. The temperature of the components also contributes. You might say the brownian motion of the air transfers the temperature, but that is one of several mechanisms. The performance in a vacuum (assuming the board doesn't quite do to other causes) would be pretty much the same.

Noise is everywhere, and in many forms. It is a function of chaos.

Manufacturers spend a lot of money trying to make radios quiet with some success. Look up S/N (signal to noise) ratio.

 

Thanks Bill,

I joined this forum to sharpen up my understanding of Electronics .

Any comments are very helpfull

 

I don't know squat about most of what boks asks about. I happened to have a handle on this one case. All those years at Collins Radio don'tcha know.

BTW, Welcome to AAC. We're an eclectic bunch, so have fun.

 

I have been playing with amateur radio for 20 years and was a keen QSL sender in the 1980's.
I now use Hamsphere.com a virtual radio that lets you speak to radio hams all over the world.
Its too cold to sit out in the Shack this time of year, lol

 

1. You need bigger tubes in your transmitter.

2. Route some of that RF into the shack. RF can heat things up nicely.

Joking.