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

ضع في اعتبارك جزيئات الغاز N التي نصف قطرها r تتحرك بشكل عشوائي مع السرعة v في الحجم الأسطواني V. عندما يصطدم جزيء بجزيء آخر ، تكون المسافة بين مراكزها 2r.
تخيل أسطوانة نصف قطرها 2r ، بمحور مواز لسرعة الجزيء. عندما ينتقل الجزيء لفترة زمنية صغيرة ويصطدم داخل الأسطوانة ، يمكن تحديد عدد الاصطدامات لكل وحدة زمنية.
باستخدام معادلة متوسط السرعة النسبية ، يمكن تحديد الاصطدامات لجميع الجزيئات المتحركة لكل وحدة زمنية.
يعطي مقلوب المعادلة متوسط الوقت بين الاصطدامات ، والمعروف باسم متوسط وقت الفراغ.
وفي الوقت نفسه ، فإن متوسط المسار الحر لجزيء الغاز هو نتاج سرعة الجزيء ومتوسط الوقت بين الاصطدامات. من خلال استبدال المصطلحات ، يمكن تحديد متوسط المسار الحر ، والذي يتناسب عكسيا مع عدد الجزيئات لكل وحدة حجم ومساحة المقطع العرضي للجزيء.
باستدعاء معادلة الغاز المثالي واستبدال المصطلحات ، يمكن الحصول على الخصائص العيانية للغاز.

<ol>
	<li>يونغ ، إتش دي وفريدمان ، ر. (2012). الفيزياء الجامعية مع الفيزياء الحديثة. سان فرانسيسكو ، كاليفورنيا: بيرسون. ص 630</li>
	<li>OpenStax. (2019). جامعة الفيزياء المجلد 1. [نسخة الويب]. تم الاسترجاع من <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>

يعني المسار الحر ويعني وقت الفراغ

<div style="direction:rtl">تأمل جزيئات الغاز الموجودة في الأسطوانة. وهي تتحرك في حركة عشوائية حيث تصطدم ببعضها البعض وتغير سرعتها واتجاهها. يُعرف متوسط جميع أطوال المسار بين الاصطدامات باسم "متوسط المسار الحر". <img alt="Equation1" src="/files/ftp_upload/14168/14168_Equation_1_new.svg" style="text-align: center; height: 40px;"> يختلف متوسط المسار الحر عكسًا مع كثافة الجزيئات لأنه عندما يكون هناك المزيد من الجزيئات داخل الحجم، يكون لديها فرصة أكبر للتصادم مع بعضها البعض، وبالتالي يقلل متوسط المسار الحر. بالإضافة إلى ذلك، يرتبط متوسط المسار الحر عكسيًا بقطر الجزيئات، لأنها إذا كانت كتلًا نقطية، فلن تتصادم أبدًا. وبالتالي، ترتبط الجزيئات الأكبر بمسار حر متوسط أقصر. يتوسع الغاز عندما ترتفع درجة الحرارة تحت ضغط ثابت؛ وبالتالي، يزداد متوسط المسافة بين الجزيئات ومتوسط المسار الحر. ومع ذلك، عند زيادة الضغط عند درجة حرارة ثابتة، ينضغط الغاز، مما يؤدي إلى انخفاض في متوسط المسار الحر. يمكن تعريف متوسط المسار الحر على أنه حاصل ضرب متوسط السرعة المتجهة المتجهة المتجهة المتجهة ومتوسط وقت الفراغ، حيث يكون متوسط وقت الفراغ هو متوسط الوقت بين الاصطدامات. 

 لنفترض أن ذرات الأرجون كتلتها المولية 39.9 جم/مول تتحرك عشوائيًا في أسطوانة عند درجة حرارة 273 كلفن وضغط 1 جو. إذا أخذنا نصف قطر ذرة الأرجون ليكون 1.70 × 10-10m، تحديد متوسط وقت الفراغ لذرات الأرجون.

 لحل المشكلة، حدد أولاً الكميات المعروفة وغير المعروفة، وقم بتحويلها إلى وحدات النظام الدولي. ثانيًا، تذكر معادلة سرعة RMS لجزيئات الغاز. ومن خلال استبدال القيم، يمكن تحديد سرعة RMS على النحو التالي: <img alt="Equation2" src="/files/ftp_upload/14168/14168_Equation_2_new.svg" style="text-align: center; height: 45px;"> وأخيرًا، تذكر معادلة متوسط وقت الفراغ. ومن خلال استبدال القيم، يمكن تحديد متوسط وقت الفراغ على النحو التالي: <img alt="Equation3" src="/files/ftp_upload/14168/14168_Equation_3_new.svg" style="text-align: center; height: 40px;"></div>

ضع في اعتبارك جزيئات الغاز في الأسطوانة. يتحركون في حركة عشوائية عندما يصطدمون ببعضهم البعض ويغيرون السرعة والاتجاه. متوسط الجميع ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

The Kinetic Theory of Gases

النظرية الحركية للغازات

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system. The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists. When an equation of state cannot be written mathematically, scientists...

ideal gas equation

Gas Laws Behind the Ideal Equation

The ideal gas equation links pressure, volume, temperature, and amount of gas. It describes a hypothetical gas and is built from four empirical gas laws: Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. When these proportionalities are combined, they give one constant called the universal gas constant. This gas constant has the same value for all real gases under certain conditions. In chemical calculations, that constant is used in the ideal gas equation. The equation works...

van der waals equation

How Real Gases Deviate from Ideal Behavior

Real gases often deviate from the ideal gas law, especially at low temperatures and high pressures. The van der Waals equation improves the ideal gas model by adding two corrections that account for these real-world effects. One correction accounts for attractive forces between molecules. These forces become stronger at higher densities and lower the measured pressure, so the equation adds a pressure term based on the square of the molar density and a positive constant a. The second...

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Liquid-Gas Changes on pV Curves

pV curves show how gas pressure changes with volume. A pV diagram is a graph of pressure versus volume for the gas being studied. It helps describe how the substance behaves. When the gas acts like an ideal gas, the ideal gas equation gives the link between pressure and volume. A common pV curve is an isotherm, which is a line drawn at fixed temperature and fixed number of molecules. For an ideal gas, pressure times volume stays constant. That means volume goes down as pressure goes up. The...

kinetic theory of an ideal gas

Avogadro's Number and Gas Particle Motion

Avogadro's number and gas particle motion help explain how gases behave at the particle level. A mole is the amount of a substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. This idea came from Amedeo Avogadro, who proposed that equal volumes of gas at the same pressure and temperature contain equal numbers of molecules, no matter what the gas is. Avogadro's number is the number of molecules in one mole. Its value is 6.02 × 10^23 mol−1. This number...

molecular kinetic energy

Gas Pressure and Molecular Motion

Gas pressure comes from the motion of molecules in a container. The word gas came from a Flemish word meaning “chaos,” and J. B. van Helmont first used it to describe vapors. In a gas, molecules move in a continuous and random way. When a molecule hits a container wall, its velocity changes. The part of the velocity parallel to the wall stays the same. The part perpendicular to the wall reverses direction, but its size does not change. If the molecule’s velocity changes in the x-direction, its...

distribution of molecular speeds

Molecular Speed Curves and Vapor Pressure

Molecular speed curves show how the speeds of gas particles are spread out at a given temperature. For a gas with many molecules, this spread is predictable even though each molecule moves randomly in direction and speed. The pattern is called the Maxwell-Boltzmann distribution. Liquids have a similar speed distribution, but it is not exactly the same as in gases. This difference helps explain boiling and vapor pressure. A molecule must reach at least a certain speed, v a, to escape from the...

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maxwell-boltzmann-distribution-problem-solving

Maxwell-Boltzmann Gas Speed Ratio

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phase diagram

Water Phase Changes on a Pressure Chart

Water phase changes can be mapped on a pressure and temperature chart called a phase diagram. These plots show which phase a substance is in at different conditions. They also reveal where phase transitions happen, because the boundary lines mark the temperatures and pressures where two phases coexist. The water phase diagram shows how pressure affects boiling. As pressure rises, the boiling temperature increases gradually until it reaches 374 °C at 218 atm. A pressure cooker works this way.

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...

escape velocities of gases

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

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Gas collisions: path length and time

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