Name: why lighter gases escape earth first
Uploaded: 2023-09-18T17:11:17.000Z
Duration: 1 min 19 s
Channel: JoVE

La vitesse d’échappement est la vitesse minimale requise pour qu’un objet non propulsé échappe à l’influence de la force gravitationnelle de l’objet primaire. La magnitude de la vitesse d’échappement de la Terre est de 11,1 km/s.
À quelle température les molécules d’hydrogène atteignent-elles une vitesse efficace égale à la vitesse d’échappement de la Terre ?
Selon la théorie cinétique des gaz, l’énergie cinétique moyenne de tout gaz est liée à sa température. La masse des molécules d'hydrogène peut être calculée en prenant le rapport entre sa masse molaire et le nombre d'Avogadro.
Maintenant, en réarrangeant l’équation de l’énergie cinétique et en substituant les quantités connues, la température nécessaire pour atteindre la vitesse d’échappement est calculée.
La température estimée est supérieure de quelques ordres de grandeur à la température à haute altitude de l'atmosphère terrestre. Cela signifie que les molécules d'hydrogène ne peuvent pas s'échapper de l'atmosphère terrestre.
Cependant, lors de collisions multiples, d'importantes molécules d'hydrogène atteignent la vitesse d'échappement permettant la perte d'hydrogène de l'atmosphère terrestre.

<ol>
	<li>OpenStax. (2019). Physique universitaire Vol. 2. [Version Web]. Extrait de la section 2.2 ; pages 83-84. <a href="https://openstax.org/books/university-physics-volume-2/pages/2-2-pressure-temperature-and-rms-speed">2.2 Pression, température et vitesse RMS - Physique universitaire Volume 2 | OpenStax</a></li>
</ol>

les vitesses d'échappement des gaz

Escape Velocities of Gases

Pour échapper à la gravité de la Terre, un objet près du sommet de l'atmosphère à une altitude de 100 km doit s'éloigner de la Terre à une vitesse de 11,1 km/s. Cette vitesse est appelée la vitesse d'échappement. La température à laquelle les molécules de gaz atteignent la vitesse quadratique moyenne, qui est égale à la vitesse d'échappement, peut être estimée en utilisant l'équation de l'énergie cinétique moyenne des molécules de gaz. Selon la théorie cinétique des gaz, l'énergie cinétique moyenne des molécules de gaz est proportionnelle à sa température. Plus la température est élevée, plus la vitesse quadratique moyenne des molécules de gaz est élevée.

Pour les molécules d'hydrogène, la vitesse quadratique moyenne égale à la vitesse d'échappement est atteinte à une température de 99,7 x 102 K. Cette température est plusieurs ordres de grandeur plus élevée que la température à une altitude de 100 km de la surface de la Terre. À de telles altitudes, la température est d'environ 250 K. Cela signifie simplement que la probabilité que les molécules d'hydrogène échappent à l'atmosphère terrestre est négligeable. Cependant, d'autre part, très peu de molécules d'hydrogène restent dans l'atmosphère de la Terre. La perte d'hydrogène se produit parce que quelques molécules ont des vitesses supérieures à la vitesse d'échappement de la Terre, même à des températures normales. La vitesse d'une molécule d'hydrogène change d'une collision à l'autre ; par conséquent, à tout instant, il y a une petite mais finie chance que la vitesse de la molécule soit supérieure à la vitesse d'échappement. La chance est suffisamment élevée pour qu'au cours de la durée de vie de la Terre, presque toutes les molécules d'hydrogène présentes dans l'atmosphère aient atteint la vitesse d'échappement à haute altitude et se soient échappées de l'attraction gravitationnelle de la Terre.

Cependant, les molécules plus lourdes, comme l'oxygène, l'azote et l'eau, ont des vitesses quadratiques moyennes plus faibles, il est donc beaucoup moins probable que l'une d'entre elles ait des vitesses supérieures à la vitesse d'échappement. La probabilité est tellement faible que des milliards d'années sont nécessaires pour perdre des quantités significatives de molécules plus lourdes de l'atmosphère. L'absence d'atmosphère sur la lune peut être expliquée en utilisant le même concept. Comme la force gravitationnelle de la lune est beaucoup plus faible, elle a perdu presque toute son atmosphère.

Les vitesses d'échappement des gaz

Pour échapper à la gravité terrestre, un objet situé près du sommet de l'atmosphère à une altitude de 100 km doit s'éloigner de la Terre à 11,1 km/s. Cette vitesse ...

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The Kinetic Theory of Gases

La théorie cinétique des gaz

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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. For hydrogen molecules, the temperature needed for rms speed to match escape velocity is 99.7 x 10 2 K.

That temperature is far above the temperature at 100 km altitude, which is about 250 K. So under normal conditions, the chance of hydrogen molecules escaping Earth’s atmosphere is very small. Even so, a few hydrogen molecules are still lost over time. Their speeds change from one collision to the next, so at any moment some molecules can move faster than escape velocity.

Over Earth’s lifetime, that small chance has been enough for almost all hydrogen molecules to escape from the atmosphere. Heavier molecules such as oxygen, nitrogen, and water move more slowly on average. That makes it much less likely that they will exceed escape velocity. Because of this, billions of years are needed to lose large amounts of these heavier gases.

The Moon shows the same idea in a stronger way. Its gravitational pull is much weaker than Earth’s. As a result, it has lost almost its entire atmosphere.

Why Lighter Gases Escape Earth First

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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pv-diagrams

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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...

maxwell-boltzmann distribution: problem solving

maxwell-boltzmann-distribution-problem-solving

Maxwell-Boltzmann Gas Speed Ratio

The Maxwell-Boltzmann distribution describes how molecular speeds are spread in a gas. Even though individual molecules move in random directions, the whole gas has a predictable speed pattern. This distribution is written as f(v), where v is molecular speed. The distribution function is used to find the expected number of particles with speeds between v1 and v2. Because N is dimensionless, f(v) has units of seconds per meter. The relationship can also be written in differential form for speed...

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: 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...

heat capacity: problem-solving

Heat Capacity of Gases by Degrees of Freedom

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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

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

Explore how escape velocity, temperature, and molecular speed affect atmospheric loss. See why hydrogen escapes more easily than heavier gases.

Why Lighter Gases Escape Earth First | JoVE K12

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Why Lighter Gases Escape Earth First

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