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

半径rのN個の気体分子が、円筒形の体積V内を速度vでランダムに移動するとします。ある分子が別の分子と衝突すると、それらの中心間の距離は2rになります。
半径が 2r の円柱で、軸が分子の速度に平行であると想像してください。分子が短い時間間隔で移動し、円筒内で衝突すると、単位時間あたりの衝突回数を決定できます。
平均相対速度方程式を使用して、単位時間あたりに移動するすべての分子の衝突を決定できます。
方程式の逆数は、平均自由時間として知られる衝突間の平均時間を示します。
一方、気体分子の平均自由行程は、分子の速度と衝突間の平均時間の積です。項を代入することにより、単位体積あたりの分子数と分子の断面積に反比例する平均自由行程を決定できます。
理想気体方程式を思い出し、項を代入すると、気体の巨視的な性質を得ることができます。

<ol>
	<li>ヤング、HD、フリードマン、RA(2012)。現代物理学と大学物理学。カリフォルニア州サンフランシスコ:ピアソン。630ページ</li>
	<li>OpenStaxです。(2019). 大学物理学 Vol.1.【Web版】。<a href="https://openstax.org/books/college-physics-2e/pages/13-4-kinetic-theory-atomic-and-molecular-explanation-of-pressure-and-temperature"から取得>https://openstax.org/books/college-physics-2e/pages/13-4-kinetic-theory-atomic-and-molecular-explanation-of-pressure-and-temperature</a></li>
</ol>

平均自由行程と平均自由時間

シリンダー内のガス分子を考えてみましょう。 それらは互いに衝突し、速度と方向を変えながらランダムな動きをします。 衝突間のすべての経路長の平均は、「平均自由行程」として知られています。

<img alt="Equation1" src="/files/ftp_upload/14168/14168_Equation_1_new.svg" style="text-align: center; height: 40px;" />

平均自由行程は分子の密度に反比例して変化します。これは、ボリューム内に分子が多くなると、分子が互いに衝突する可能性が高くなり、平均自由行程が減少するためです。 さらに、分子が点質量であれば決して衝突しないため、平均自由行程は分子の直径に反比例します。 したがって、分子が大きいほど、平均自由行程は短くなります。

一定の圧力下で温度が上昇すると、ガスは膨張します。 したがって、分子間の平均距離と平均自由行程が増加します。 ただし、一定の温度で圧力が増加すると、ガスが圧縮され、平均自由行程が減少します。 平均自由行程は、平均速度と平均自由時間の積として定義できます。ここで、平均自由時間は衝突間の平均時間です。

モル質量 39.9 g/mol のアルゴン原子が、温度 273 K、圧力 1 atm の円筒内でランダムに移動していると考えてみましょう。 アルゴン原子の半径を 1.70 × とすると、 10-10m、アルゴン原子の平均自由時間を決定します。

この問題を解決するには、まず既知の量と未知の量を特定し、それらを SI 単位に変換します。

次に、気体分子の RMS 速度方程式を思い出してください。 値を代入することで、RMS 速度を次のように決定できます。

<img alt="Equation2" src="/files/ftp_upload/14168/14168_Equation_2_new.svg" style="text-align: center; height: 45px;" />

最後に、平均自由時間の方程式を思い出してください。 値を代入すると、平均自由時間は次のように決定できます。

<img alt="Equation3" src="/files/ftp_upload/14168/14168_Equation_3_new.svg" style="text-align: center; height: 40px;" />

シリンダー内のガス分子を考えてみましょう。それらは互いに衝突し、速度と方向を変えるときにランダムな動きで動きます。すべての平均...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

The Kinetic Theory of Gases

気体分子運動論

KEY TERMS AND CONCEPTS

主要用語と概念

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

equation of state

Gas Behavior in the Equation of State

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maxwell-boltzmann-distribution-problem-solving

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Water Phase Changes on a Pressure Chart

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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...

heat capacity: problem-solving

Heat Capacity of Gases by Degrees of Freedom

Heat capacity of gases depends on the gas type and the motion of its molecules. It is the amount of heat energy needed to raise the temperature of a unit mass of gas by one degree Celsius. This thermodynamic property is important in science and industry. To solve heat capacity problems, first identify the gas. A gas's molecular structure affects its heat capacity because the molecules have different degrees of freedom. These values can be found from tables or from empirical equations. Next,...

dalton's law of partial pressure

Gas Mixtures and Their Partial Pressures

Gas mixtures have a total pressure that comes from the partial pressures of each gas. A partial pressure is the pressure one gas would make if it filled the whole container by itself. This idea helps explain how gases behave when they are mixed together. When two or more gases share a container, their molecules move randomly and collide with one another. If the gases are at the same temperature, they reach thermal equilibrium. Their molecules then have the same average kinetic energy. In that...

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Why Lighter Gases Escape Earth First

Earth’s escape velocity is the speed an object needs to leave gravity behind. Near the top of the atmosphere, about 100 km above Earth, that speed is 11.1 km/s. Gas molecules can escape only if their speeds become high enough to reach that limit. The chance of escape depends on gas temperature and molecular speed. According to kinetic theory, the average kinetic energy of gas molecules is proportional to temperature. As temperature rises, the rms speed, or root-mean-square speed, also rises.

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

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

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Gas collisions: path length and time

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