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

La velocità di fuga è la velocità minima richiesta a un oggetto non spinto per sfuggire all'influenza della forza gravitazionale dell'oggetto primario. L'ampiezza della velocità di fuga della Terra è di 11,1 km/s.
Qual è la temperatura alla quale le molecole di idrogeno raggiungono la velocità rms uguale alla velocità di fuga della Terra?
Secondo la teoria cinetica dei gas, l'energia cinetica media di qualsiasi gas è correlata alla sua temperatura. La massa delle molecole di idrogeno può essere calcolata prendendo il rapporto tra la sua massa molare e il numero di Avogadro.
Ora, riorganizzando l'equazione per l'energia cinetica e sostituendo le quantità note, viene calcolata la temperatura richiesta per raggiungere la velocità di fuga.
La temperatura stimata è di alcuni ordini di grandezza superiore alla temperatura ad alta quota dell'atmosfera terrestre. Ciò significa che le molecole di idrogeno non possono sfuggire dall'atmosfera terrestre.
Tuttavia, durante le collisioni multiple, le molecole di idrogeno significative raggiungono la velocità di fuga che consente la perdita di idrogeno dall'atmosfera terrestre.

<ol>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. Estratto dalla sezione 2.2; pagina 83-84. <a href="https://openstax.org/books/university-physics-volume-2/pages/2-2-pressure-temperature-and-rms-speed">2.2 Pressione, Temperatura e Velocità RMS - Fisica Universitaria Volume 2 | OpenStax</a></li>
</ol>

velocità di fuga dei gass

Escape Velocities of Gases

Per sfuggire alla gravità terrestre, un oggetto vicino alla sommità dell'atmosfera, ad un'altitudine di 100 km, deve muoversi via dalla Terra alla velocità di 11.1 km/s. Questa velocità è chiamata velocità di fuga. La temperatura alla quale le molecole di gas raggiungono la velocità quadratica media, che è uguale alla velocità di fuga, può essere stimata utilizzando l'equazione per l'energia cinetica media delle molecole del gas. Secondo la teoria cinetica dei gas, l'energia cinetica media delle molecole del gas è proporzionale alla sua temperatura. Più alta è la temperatura, maggiore è la velocità quadratica media delle molecole del gas.

Per le molecole di idrogeno, la velocità quadratica media uguale alla velocità di fuga è raggiunta ad una temperatura di 99.7 x 102 K. Questa temperatura è di diversi ordini di grandezza più alta rispetto alla temperatura ad un'altitudine di 100 km dalla superficie terrestre. A queste altitudini, la temperatura è approssimativamente di 250 K. Ciò significa semplicemente che la probabilità che le molecole di idrogeno sfuggano dall'atmosfera terrestre è trascurabile. Tuttavia, al contrario, rimangono pochissime molecole di idrogeno nell'atmosfera terrestre. La perdita di idrogeno avviene perché alcune molecole hanno velocità superiori alla velocità di fuga della Terra, anche a temperature normali. La velocità di una molecola di idrogeno cambia da una collisione alla successiva; quindi, in ogni istante, c'è una piccola ma finita possibilità che la velocità della molecola sia maggiore della velocità di fuga. La probabilità è abbastanza alta che nel corso della vita della Terra, quasi tutte le molecole di idrogeno nell'atmosfera abbiano raggiunto la velocità di fuga ad alte altitudini ed siano sfuggite alla forza di gravità terrestre.

Ciononostante, molecole più pesanti, come l'ossigeno, l'azoto e l'acqua, hanno velocità quadratiche medie inferiori, quindi è molto meno probabile che una qualsiasi di esse abbia velocità superiori alla velocità di fuga. La probabilità è così piccola che sono necessari miliardi di anni per perdere quantità significative di molecole più pesanti dall'atmosfera. La mancanza di atmosfera della luna può essere spiegata utilizzando lo stesso concetto. Siccome l'attrazione gravitazionale della Luna è molto più debole, ha perso quasi tutta la sua atmosfera.

Velocità di fuga dei gass

Per sfuggire alla gravità terrestre, un oggetto vicino alla parte superiore dell'atmosfera a un'altitudine di 100 km deve allontanarsi dalla Terra a 11,1 km/s. Questa velocità ...

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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

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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

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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