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

Considere N moléculas de gas con radio r que se mueven aleatoriamente con velocidad v en un volumen cilíndrico V. Cuando una molécula colisiona con otra molécula, la distancia entre sus centros es de 2r.
Imagina un cilindro con un radio de 2r, con un eje paralelo a la velocidad de la molécula. Cuando la molécula viaja por un pequeño intervalo de tiempo y colisiona dentro del cilindro, se puede determinar el número de colisiones por unidad de tiempo.
Usando la ecuación de velocidad relativa promedio, se pueden determinar las colisiones de todas las moléculas en movimiento por unidad de tiempo.
El recíproco de la ecuación da el tiempo medio entre colisiones, conocido como tiempo libre medio.
Mientras tanto, el camino libre medio de una molécula de gas es el producto de la velocidad de la molécula y el tiempo promedio entre colisiones. Al sustituir los términos, se puede determinar el camino libre medio, que es inversamente proporcional al número de moléculas por unidad de volumen y al área de la sección transversal de la molécula.
Recordando la ecuación del gas ideal y sustituyendo los términos, se pueden obtener las propiedades macroscópicas del gas.

<ol>
	<li>Young, H.D y Freedman, R.A. (2012). Física Universitaria con Física Moderna. San Francisco, CA: Pearson. Págs. 630</li>
	<li>OpenStax. (2019). Física Universitaria Vol. 1. [Versión web]. Obtenido 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>

camino libre medio y tiempo libre medio

Considera las moléculas de gas en un cilindro. Se mueven en un movimiento aleatorio mientras chocan entre sí y cambian de velocidad y dirección. El promedio de todas las longitudes de camino entre colisiones se conoce como el "camino libre medio". <img alt="Equation1" src="/files/ftp_upload/14168/14168_Equation_1_new.svg" style="text-align: center; height: 40px;"> El camino libre medio varía inversamente con la densidad de las moléculas porque cuando hay más moléculas dentro de un volumen, tienen una mayor probabilidad de colisionar entre sí, reduciendo así el camino libre medio. Además, el camino libre medio está inversamente relacionado con el diámetro de las moléculas porque si fueran masas puntuales, nunca colisionarían. Por lo tanto, las moléculas más grandes están asociadas con un camino libre medio más corto. El gas se expande cuando la temperatura aumenta bajo presión constante; así, la distancia promedio entre moléculas y el camino libre medio aumentan. Sin embargo, cuando la presión se aumenta a temperatura constante, el gas se comprime, lo que lleva a una disminución en el camino libre medio. El camino libre medio se puede definir como el producto de la velocidad promedio y el tiempo libre medio, donde el tiempo libre medio es el tiempo promedio entre colisiones. Considera átomos de argón con una masa molar de 39.9 g/mol moviéndose al azar en un cilindro a una temperatura de 273 K y una presión de 1 atm. Tomando el radio de un átomo de argón como 1.70 × 10-10 m, determina el tiempo libre medio para los átomos de argón. Para resolver el problema, primero identifica las magnitudes conocidas y desconocidas, y conviértelas en unidades del SI. En segundo lugar, recuerda la ecuación de la velocidad RMS para las moléculas de gas. Al sustituir los valores, la velocidad RMS se puede determinar de la siguiente manera: <img alt="Equation2" src="/files/ftp_upload/14168/14168_Equation_2_new.svg" style="text-align: center; height: 45px;"> Por último, recuerda la ecuación del tiempo libre medio. Al sustituir los valores, el tiempo libre medio se puede determinar de la siguiente manera: <img alt="Equation3" src="/files/ftp_upload/14168/14168_Equation_3_new.svg" style="text-align: center; height: 40px;">

Camino libre medio y tiempo libre medio

Considere las moléculas de gas en un cilindro. Se mueven en un movimiento aleatorio a medida que chocan entre sí y cambian de velocidad y dirección. El promedio de todos los ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

The Kinetic Theory of Gases

La teoría cinética de los gases

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

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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...

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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

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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

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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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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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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.

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Gas collisions: path length and time

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