We're studying the kinetic theory of gases in school, and one of the points that was brought up was that: "Gases consist of particles in constant, random motion." How is it possible for gas particles to move in straight lines, entirely randomly? Doesn't gravity affect them, or is their mass so small that its effect on their movement is negligible?
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1$\begingroup$ It's not due to their small mass since everything at this height experiences about the same gravitational acceleration. $\endgroup$– JobHunter69Commented Sep 29, 2016 at 0:51
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1$\begingroup$ Yes, they do, and when you consider it, you get the barometric formula back. $\endgroup$– GregCommented Sep 29, 2016 at 10:21
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$\begingroup$ Curved motion need not be any less random. In fact, this begs the question, what do you understand by "random"? It is the orientation (direction) of the trajectory that might be regarded as random. In addition, that orientational probability is nearly uniform (isotropic). $\endgroup$– Buck Thorn ♦Commented Apr 2, 2020 at 16:33
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2 Answers
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Yes gravity pulls on gas molecules. That is why the atmosphere doesn't just float off into space.
The gist is that the time between collisions is very short in the lower atmosphere, and the distances very short. The mean free path at atmospheric pressure is only about 70 nanometers. So the assumption is that gas particles travel in a straight line between collisions.
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1$\begingroup$ In contrast, imagine gas molecules on the moon, bouncing around like isolated balls as they are likely to hit the ground again before another gas molecule; or the situation up where the space station orbits: a molecule tossed upward will make a suborbital arc befome coming back down to where the air is thicker and hitting something. $\endgroup$– JDługoszCommented Sep 29, 2016 at 6:46
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3$\begingroup$ Suppose an air molecule travels by $500~\mathrm{m}/\mathrm{s}$ (or $500$ nanometers per nanosecond, if you prefer). The rough time scale for gravity to interfere with that, would be found by dividing by $10~\mathrm{m}/\mathrm{s}^2$, so it is of order tens of seconds before gravity will disturb a body of that velocity much. However, with the number from the above answer, we see that the molecule hits another one every $0.14$ nanoseconds. So the deviation from straight line paths will be negligible. $\endgroup$ Commented Sep 29, 2016 at 9:12
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To add to previous answers, all molecules and atoms are affected by gravity and so the density of the atmosphere is greater at the surface of the earth compared to higher up, which is why climbing on Everest most climbers take extra oxygen (although, remarkably, it has been done without this aid).
At room temperature gas molecules have an average thermal energy of $3RT/2$ ($R$ is the gas constant $8.314 \pu{ J mol^{-1} K^{-1}}$) and thus they have some kinetic energy and can jostle around in a random manner.
As there is nothing but empty space between one collision of a gas molecule and another, by Newton's law they would travel in straight lines at constant velocity if no force is applied. Now there is a force and this is gravity acting downwards but over the very small distance between collisions in a gas in a room, the effect is negligible. Thus we say that they travel in 'straight lines' but remember that this is only an approximation, but a very good one.
(Notes: The collisions are called 'elastic' which means that no energy is retained within either molecule after the collision compared to that before it. There is also a distribution of velocities, the Maxwell-Boltzmann distribution, or speed the Maxwell distribution).
