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

ניקח לדוגמה מולקולות גז N עם רדיוס r הנעות באופן אקראי במהירות v בנפח גלילי V. כאשר מולקולה אחת מתנגשת במולקולה אחרת, המרחק בין המרכזים שלה הוא 2r.
דמיינו גליל עם רדיוס של 2r, עם ציר מקביל למהירות המולקולה. כאשר המולקולה נעה למרווח זמן קטן ומתנגשת בתוך הצילינדר, ניתן לקבוע את מספר ההתנגשויות ליחידת זמן.
באמצעות משוואת המהירות היחסית הממוצעת, ניתן לקבוע את ההתנגשויות של כל המולקולות הנעות ליחידת זמן.
יחסי הגומלין של המשוואה נותנים את הזמן הממוצע בין התנגשויות, המכונה הזמן הפנוי הממוצע.
בינתיים, הנתיב החופשי הממוצע של מולקולת גז הוא מכפלה של מהירות המולקולה והזמן הממוצע בין התנגשויות. על ידי החלפת המונחים, ניתן לקבוע את הנתיב החופשי הממוצע, שהוא ביחס הפוך למספר המולקולות ליחידת נפח ולשטח החתך של המולקולה.
אם זוכרים את משוואת הגז האידיאלי ומחליפים את המונחים, ניתן לקבל את התכונות המקרוסקופיות של הגז.

<ol>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: פירסון. עמ' 630</li>
	<li>OpenStax. (2019). פיזיקה אוניברסיטאית כרך 1. [גרסת אינטרנט]. מקור: <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>

נתיב חופשי מתכוון וזמן פנוי מתכוון

<div style="direction:rtl">שקול את מולקולות הגז בצילינדר. הם נעים בתנועה אקראית כשהם מתנגשים זה בזה ומשנים מהירות וכיוון. הממוצע של כל אורכי הנתיב בין התנגשויות ידוע כ-"הנתיב החופשי הממוצע." <img alt="Equation1" src="/files/ftp_upload/14168/14168_Equation_1_new.svg" style="text-align: center; height: 40px;"> הנתיב החופשי הממוצע משתנה הפוך לצפיפות המולקולות מכיוון שכאשר יש יותר מולקולות בתוך נפח, יש להן סיכוי גדול יותר להתנגש זו בזו, ובכך להפחית את הנתיב החופשי הממוצע. בנוסף, הנתיב החופשי הממוצע עומד ביחס הפוך לקוטר המולקולות מכיוון שאם הן היו מסות נקודתיות, הן לעולם לא היו מתנגשות. לפיכך, מולקולות גדולות יותר קשורות לנתיב חופשי ממוצע קצר יותר. הגז מתרחב כאשר הטמפרטורה עולה בלחץ קבוע; לפיכך, המרחק הממוצע בין מולקולות לנתיב החופשי הממוצע גדל. עם זאת, כאשר הלחץ מוגבר בטמפרטורה קבועה, הגז נדחס, מה שמוביל לירידה בנתיב החופשי הממוצע. ניתן להגדיר את הנתיב הפנוי הממוצע כמכפלת המהירות הממוצעת והזמן הפנוי הממוצע, כאשר הזמן הפנוי הממוצע הוא הזמן הממוצע בין התנגשויות. שקול אטומי ארגון עם מסה מולרית של 39.9 גרם/מול זזים באקראי בגליל בטמפרטורה של 273 K ולחץ של 1 אטמוספירה. הרדיוס של אטום ארגון הוא 1.70 × 10-10מ', קבע את הזמן הפנוי הממוצע עבור אטומי ארגון. כדי לפתור את הבעיה, זהה תחילה את הכמויות הידועות והלא ידועות, והמר אותן ליחידות SI. שנית, זכור את משוואת המהירות RMS עבור מולקולות גז. על ידי החלפת הערכים, ניתן לקבוע את מהירות ה-RMS באופן הבא: <img alt="Equation2" src="/files/ftp_upload/14168/14168_Equation_2_new.svg" style="text-align: center; height: 45px;"> לבסוף, זכור את משוואת הזמן הפנוי הממוצע. על ידי החלפת הערכים, ניתן לקבוע את הזמן הפנוי הממוצע באופן הבא: <img alt="Equation3" src="/files/ftp_upload/14168/14168_Equation_3_new.svg" style="text-align: center; height: 40px;"></div>

חשבו על מולקולות הגז בצילינדר. הם נעים בתנועה אקראית כשהם מתנגשים זה בזה ומשנים מהירות וכיוון. הממוצע של כל ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

The Kinetic Theory of Gases

התיאוריה הקינטית של הגזים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

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van der waals equation

How Real Gases Deviate from Ideal Behavior

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kinetic theory of an ideal gas

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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...

maxwell-boltzmann distribution: problem solving

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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