Name: gas collisions: path length and time
Uploaded: 2025-05-22T09:05:59.000Z
Duration: 1 min 22 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.12

SC.912.P.12.10

Mean free path and Mean free time

Considérons N molécules de gaz de rayon r se déplaçant aléatoirement à la vitesse v dans un volume cylindrique V. Lorsqu’une molécule entre en collision avec une autre molécule, la distance entre leurs centres est de 2r.
Imaginons un cylindre de rayon de 2r, avec un axe parallèle à la vitesse de la molécule. Lorsque la molécule se déplace pendant un petit intervalle de temps et entre en collision à l’intérieur du cylindre, le nombre de collisions par unité de temps peut être déterminé.
À l’aide de l’équation de la vitesse relative moyenne, les collisions de toutes les molécules en mouvement par unité de temps peuvent être déterminées.
L’inverse de l’équation donne le temps moyen entre les collisions, connu sous le nom de temps libre moyen.
Pendant ce temps, le libre parcours moyen d'une molécule de gaz est le produit de la vitesse de la molécule et du temps moyen entre les collisions. En substituant les termes, on peut déterminer le libre parcours moyen, qui est inversement proportionnel au nombre de molécules par unité de volume et à l’aire de la section transversale de la molécule.
En rappelant l’équation du gaz idéal et en substituant les termes, les propriétés macroscopiques du gaz peuvent être obtenues.

<ol>
	<li>Young, H.D et Freedman, R.A. (2012). La physique universitaire avec la physique moderne. San Francisco, Californie : Pearson. p. 630</li>
	<li>OpenStax. (2019). Physique universitaire Vol. 1. [Version Web]. Tiré de <a href="https://openstax.org/books/college-physics-2e/pages/13-4-kinetic-theory-atomic-and-molecular-explanation-of-pressure-and-temperature">https://openstax.org/books/college-physics-2e/pages/13-4-kinetic-theory-atomic-and-molecular-explanation-of-pressure-and-temperature</a></li>
</ol>

chemin libre moyen et temps libre moyen

Considérez les molécules de gaz dans un cylindre. Elles se déplacent de manière aléatoire lorsqu'elles entrent en collision les unes avec les autres, changeant ainsi de vitesse et de direction. La moyenne de toutes les longueurs de chemin entre les collisions est appelée le "chemin libre moyen".

<img alt="Equation1" src="/files/ftp_upload/14168/14168_Equation_1_new.svg" style="text-align: center; height: 40px;" />

Le chemin libre moyen varie de manière inverse avec la densité des molécules car lorsque davantage de molécules se trouvent dans un volume, elles ont davantage de chances de se heurter les unes aux autres, réduisant ainsi le chemin libre moyen. De plus, le chemin libre moyen est inversement lié au diamètre des molécules car si elles étaient des masses ponctuelles, elles ne se heurteraient jamais. Ainsi, les molécules plus grandes sont associées à un chemin libre moyen plus court.

Le gaz se dilate lorsque la température augmente à pression constante; ainsi, la distance moyenne entre les molécules et le chemin libre moyen augmentent. Cependant, lorsque la pression est augmentée à température constante, le gaz se comprime, entraînant une diminution du chemin libre moyen. Le chemin libre moyen peut être défini comme le produit de la vitesse moyenne et du temps libre moyen, où le temps libre moyen est le temps moyen entre les collisions.

Considérons des atomes d'argon avec une masse molaire de 39,9 g/mol se déplaçant de manière aléatoire dans un cylindre à une température de 273 K et à une pression de 1 atm. En prenant le rayon d'un atome d'argon comme étant de 1,70 × 10-10 m, déterminez le temps libre moyen des atomes d'argon.

Pour résoudre le problème, identifiez d'abord les quantités connues et inconnues, et convertissez-les en unités SI.

Deuxièmement, rappellez-vous l'équation de la vitesse RMS pour les molécules de gaz. En substituant les valeurs, la vitesse RMS peut être déterminée comme suit :

<img alt="Equation2" src="/files/ftp_upload/14168/14168_Equation_2_new.svg" style="text-align: center; height: 45px;" />

Finalement, rappellez-vous l'équation du temps libre moyen. En substituant les valeurs, le temps libre moyen peut être déterminé comme suit :

<img alt="Equation3" src="/files/ftp_upload/14168/14168_Equation_3_new.svg" style="text-align: center; height: 40px;" />

Chemin libre moyen et Temps libre moyen

Considérez les molécules de gaz dans une bouteille. Ils se déplacent dans un mouvement aléatoire lorsqu’ils entrent en collision les uns avec les autres et changent de vitesse et de direction. La moyenne de tous ...

Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

The Kinetic Theory of Gases

La théorie cinétique des gaz

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

gas collisions: path length and time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions.

The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger molecules have a shorter mean free path, while point masses would never collide.

Temperature and pressure also affect the mean free path. When temperature increases at constant pressure, a gas expands. The average distance between molecules increases, and the mean free path increases too. When pressure increases at constant temperature, the gas compresses. That reduces the mean free path.

The mean free path can also be written as the product of average speed and mean free time. Mean free time is the average time between collisions. A sample problem uses argon atoms with a molar mass of 39.9 g/mol at 273 K and 1 atm. The radius of an argon atom is taken as 1.70 × 10 -10 m. To find the mean free time, first identify the known and unknown values and convert them to SI units. Then use the RMS speed equation for gas molecules. After that, substitute the values into the mean free time equation to calculate the result.

Gas collisions: path length and time

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mean free path and mean free time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions. The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger...

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key terms and concepts

Learn how gas molecule collisions determine mean free path and mean free time, and see how density, size, temperature, and pressure affect them in argon.

Gas collisions: path length and time | JoVE K12

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A. Motion can be measured and described qualitatively and quantitatively. Net forces create a change in motion. When objects travel at speeds comparable to the speed of light, Einstein's special theory of relativity applies.

B. Momentum is conserved under well-defined conditions. A change in momentum occurs when a net force is applied to an object over a time interval.

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Gas collisions: path length and time

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