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

반지름 r을 가진 N 기체 분자가 원통형 부피 V에서 속도 v로 무작위로 움직인다고 가정합니다. 한 분자가 다른 분자와 충돌할 때 중심 사이의 거리는2r입니다.
반지름이2r이고 축이 분자의 속도와 평행한 원통을 상상해 보십시오. 분자가 짧은 시간 간격으로 이동하여 실린더 내부에서 충돌할 때 단위 시간당 충돌 횟수를 결정할 수 있습니다.
평균 상대 속도 방정식을 사용하여 단위 시간당 움직이는 모든 분자에 대한 충돌을 결정할 수 있습니다.
방정식의 역수는 평균 자유 시간이라고 하는 충돌 사이의 평균 시간을 제공합니다.
한편, 기체 분자의 평균 자유 경로는 분자의 속도와 충돌 사이의 평균 시간의 곱입니다. 항을 대체함으로써 평균 자유 경로를 결정할 수 있으며, 이는 단위 부피당 분자의 수와 분자의 단면적에 반비례합니다.
이상-기체 방정식을 상기하고 항을 대체하면 기체의 거시적 특성을 얻을 수 있습니다.

<ol>
	<li>Young, H.D 및 Freedman, RA (2012). 현대 물리학을 가진 대학 물리학. 샌프란시스코, 캘리포니아 : 피어슨. 630쪽</li>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 1. [웹 버전]. 원본 주소 <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>

평균 자유 경로 및 평균 자유 시간

원통 안의 기체 분자를 생각해 보세요. 이것은 서로 충돌하면서 속도와 방향을 바꾸면서 무작위로 움직입니다. 충돌 사이의 모든 경로 길이의 평균을 '평균 자유 경로'라고 합니다.

<img alt="Equation1" src="/files/ftp_upload/14168/14168_Equation_1_new.svg" style="text-align: center; height: 40px;" />

평균 자유 행로는 분자 밀도에 반비례합니다. 왜냐하면 부피 내부에 더 많은 분자가 있으면 서로 충돌할 가능성이 더 높아져 평균 자유 행로가 줄어들기 때문입니다. 또한 평균 자유 경로는 분자의 직경과 반비례합니다. 왜냐하면 분자가 점 질량이라면 절대 충돌하지 않기 때문입니다. 따라서 분자가 클수록 평균 자유 경로가 짧아집니다.

일정한 압력 하에서 온도가 상승하면 가스가 팽창합니다. 따라서 분자 사이의 평균 거리와 평균 자유 경로가 증가합니다. 그러나 일정한 온도에서 압력을 높이면 가스가 압축되어 평균 자유 행로가 감소합니다. 평균 자유 경로는 평균 속도와 평균 자유 시간의 곱으로 정의할 수 있습니다. 여기서 평균 자유 시간은 충돌 간의 평균 시간입니다.

온도 273K', 압력 1atm의 실린더 내에서 무작위로 움직이는 몰질량 39.9g/mol의 아르곤 원자를 생각해 보세요. 아르곤 원자의 반경을 1.70 × 10-10m, 아르곤 원자의 평균 자유 시간을 결정하세요.

문제를 해결하려면 먼저 알려진 양과 알려지지 않은 양을 식별하고 이를 SI 단위로 변환하세요.

두 번째로 기체 분자의 RMS 속도 방정식을 기억해 보세요. 값을 대체하면 RMS 속도는 다음과 같이 결정될 수 있습니다.

<img alt="Equation2" src="/files/ftp_upload/14168/14168_Equation_2_new.svg" style="text-align: center; height: 45px;" />

마지막으로 평균 자유 시간 방정식을 떠올려 보세요. 값을 대체하면 평균 여유 시간은 다음과 같이 결정될 수 있습니다.

<img alt="Equation3" src="/files/ftp_upload/14168/14168_Equation_3_new.svg" style="text-align: center; height: 40px;" />

실린더 안의 기체 분자를 생각해 보십시오. 그들은 서로 충돌하고 속도와 방향을 바꾸면서 무작위 동작으로 움직입니다. 모두의 평균 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

The Kinetic Theory of Gases

기체 분자 운동론

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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kinetic theory of an ideal gas

Avogadro's Number and Gas Particle Motion

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molecular kinetic energy

Gas Pressure and Molecular Motion

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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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