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

Die Fluchtgeschwindigkeit ist die minimale Geschwindigkeit, die erforderlich ist, damit ein nicht angetriebenes Objekt dem Einfluss der Gravitationskraft des Primärobjekts entkommen kann. Die Größe der Fluchtgeschwindigkeit der Erde beträgt 11,1 km/s.
Bei welcher Temperatur erreichen Wasserstoffmoleküle die Effektivgeschwindigkeit, die der Fluchtgeschwindigkeit der Erde entspricht?
Nach der kinetischen Theorie der Gase hängt die durchschnittliche kinetische Energie eines Gases mit seiner Temperatur zusammen. Die Masse von Wasserstoffmolekülen kann berechnet werden, indem man das Verhältnis seiner Molmasse zur Avogadro-Zahl nimmt.
Wenn man nun die Gleichung für die kinetische Energie neu anordnet und die bekannten Größen einsetzt, wird die Temperatur berechnet, die zum Erreichen der Fluchtgeschwindigkeit erforderlich ist.
Die geschätzte Temperatur ist einige Größenordnungen höher als die Temperatur in großen Höhen der Erdatmosphäre. Das bedeutet, dass die Wasserstoffmoleküle nicht aus der Erdatmosphäre entweichen können.
Bei mehreren Kollisionen erreichen jedoch signifikante Wasserstoffmoleküle die Fluchtgeschwindigkeit, die den Verlust von Wasserstoff aus der Erdatmosphäre ermöglicht.

<ol>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Webversion]. Abgerufen aus Abschnitt 2.2; Seite 83-84. <a href="https://openstax.org/books/university-physics-volume-2/pages/2-2-pressure-temperature-and-rms-speed">2.2 Druck, Temperatur und RMS-Geschwindigkeit - University Physics Volume 2 | OpenStax</a></li>
</ol>

fluchtgeschwindigkeiten von gasen

Escape Velocities of Gases

Um der Schwerkraft der Erde zu entkommen, muss sich ein Objekt in der Nähe des oberen Teils der Atmosphäre in einer Höhe von 100 km mit einer Geschwindigkeit von 11,1 km/s von der Erde entfernen. Diese Geschwindigkeit wird Fluchtgeschwindigkeit genannt. Die Temperatur, bei der Gas-Moleküle die mittlere Geschwindigkeit erreichen, die gleich der Fluchtgeschwindigkeit ist, kann mit der Gleichung für die mittlere kinetische Energie der Gas-Moleküle abgeschätzt werden. Gemäß der kinetischen Theorie der Gase ist die mittlere kinetische Energie der Gas-Moleküle proportional zu ihrer Temperatur. Je höher die Temperatur, desto höher die mittlere Geschwindigkeit der Gas-Moleküle.

Für Wasserstoff-Moleküle wird die mittlere Geschwindigkeit, die der Fluchtgeschwindigkeit entspricht, bei einer Temperatur von 99,7 × 10^2 K erreicht. Diese Temperatur ist um einige Größenordnungen höher als die Temperatur in 100 km Höhe über der Erdoberfläche. In solchen Höhen beträgt die Temperatur etwa 250 K. Das bedeutet einfach, dass die Wahrscheinlichkeit, dass Wasserstoff-Moleküle der Erdatmosphäre entkommen, vernachlässigbar ist. Auf der anderen Seite sind jedoch sehr wenige Wasserstoff-Moleküle in der Erdatmosphäre vorhanden. Der Verlust von Wasserstoff tritt auf, weil einige Moleküle auch bei normalen Temperaturen Geschwindigkeiten haben, die höher als die Fluchtgeschwindigkeit der Erde sind. Die Geschwindigkeit eines Wasserstoff-Moleküls ändert sich von einer Kollision zur nächsten; daher besteht zu jedem Zeitpunkt eine geringe, aber endliche Chance, dass die Geschwindigkeit des Moleküls größer als die Fluchtgeschwindigkeit ist. Die Chance ist hoch genug, dass im Laufe der Erdgeschichte fast alle Wasserstoff-Moleküle in der Atmosphäre die Fluchtgeschwindigkeit in großen Höhen erreicht und der Anziehungskraft der Erde entkommen sind.

Schwerere Moleküle wie Sauerstoff, Stickstoff und Wasser haben jedoch geringere mittlere Geschwindigkeiten, sodass es viel unwahrscheinlicher ist, dass sie Geschwindigkeiten größer als die Fluchtgeschwindigkeit aufweisen. Die Wahrscheinlichkeit ist so gering, dass Milliarden von Jahren erforderlich sind, um signifikante Mengen schwererer Moleküle aus der Atmosphäre zu verlieren. Das Fehlen einer Atmosphäre auf dem Mond lässt sich mit demselben Konzept erklären. Da die Anziehungskraft des Mondes deutlich schwächer ist, hat er fast seine gesamte Atmosphäre verloren.

Fluchtgeschwindigkeiten von Gasen

Um der Schwerkraft der Erde zu entkommen, muss sich ein Objekt in der Nähe des oberen Randes der Atmosphäre in einer Höhe von 100 km mit 11,1 km/s von der Erde entfernen. Diese Geschwindigkeit ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

The Kinetic Theory of Gases

Die kinetische Gastheorie

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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

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...

pv-diagrams

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...

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

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

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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JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Why Lighter Gases Escape Earth First

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