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

A velocidade de escape é a velocidade mínima necessária para que um objeto não propelido escape da influência da força gravitacional do objeto primário. A magnitude da velocidade de escape da Terra é de 11,1 km/s.
Qual é a temperatura na qual as moléculas de hidrogênio atingem a velocidade rms igual à velocidade de escape da Terra?
De acordo com a teoria cinética dos gases, a energia cinética média de qualquer gás está relacionada à sua temperatura. A massa das moléculas de hidrogênio pode ser calculada tomando a razão entre sua massa molar e o número de Avogadro.
Agora, reorganizando a equação da energia cinética e substituindo as quantidades conhecidas, a temperatura necessária para atingir a velocidade de escape é calculada.
A temperatura estimada é algumas ordens de magnitude mais alta do que a temperatura em grandes altitudes da atmosfera da Terra. Isso significa que as moléculas de hidrogênio não podem escapar da atmosfera da Terra.
No entanto, durante colisões múltiplas, moléculas de hidrogênio significativas atingem a velocidade de escape, permitindo a perda de hidrogênio da atmosfera da Terra.

<ol>
	<li>OpenStax. (2019). Física Universitária Vol. 2. [Versão Web]. Obtido da seção 2.2; página 83-84. <a href="https://openstax.org/books/university-physics-volume-2/pages/2-2-pressure-temperature-and-rms-speed">2.2 Pressão, Temperatura e Velocidade RMS - University Physics Volume 2 | OpenStax</a></li>
</ol>

velocidades de escape de gases

Escape Velocities of Gases

Para escapar da gravidade da Terra, um objeto próximo ao topo da atmosfera, a uma altitude de 100 km, deve se afastar da Terra a 11,1 km/s. Essa velocidade é chamada de velocidade de escape. A temperatura na qual as moléculas de gás atingem uma velocidade quadrática média que é igual à velocidade de escape pode ser estimada usando a equação para a energia cinética média das moléculas de gás. De acordo com a teoria cinética dos gases, a energia cinética média das moléculas de gás é proporcional à sua temperatura. Quanto maior a temperatura, maior a velocidade quadrática média das moléculas de um gás.

Para moléculas de hidrogênio, a velocidade quadrática média igual à velocidade de escape é atingida a uma temperatura de 99,7 x 102 K. Essa temperatura é algumas ordens de magnitude mais alta em comparação com a temperatura a uma altitude de 100 km da superfície da Terra. Em tais altitudes, a temperatura é de aproximadamente 250 K. Isso simplesmente significa que a probabilidade de moléculas de hidrogênio escaparem da atmosfera da Terra é negligível. No entanto, ao contrário do esperado, restam muito poucas moléculas de hidrogênio na atmosfera da Terra. A perda de hidrogênio ocorre porque algumas moléculas possuem velocidades maiores do que a velocidade de escape da Terra, mesmo em temperaturas normais. A velocidade de uma molécula de hidrogênio muda de uma colisão para a próxima; portanto, em qualquer instante, há uma pequena, mas finita, chance de que a velocidade da molécula seja maior do que a velocidade de escape. A chance é alta o suficiente para que, ao longo da vida da Terra, quase todas as moléculas de hidrogênio da atmosfera tenham atingido a velocidade de escape em altitudes elevadas e escapado da atração gravitacional da Terra.

No entanto, moléculas mais pesadas, como oxigênio, nitrogênio e água, têm velocidades quadráticas médias menores, portanto, é muito menos provável que alguma delas tenha velocidades maiores do que a velocidade de escape. A probabilidade é tão pequena que bilhões de anos são necessários para perder quantidades significativas de moléculas mais pesadas da atmosfera. A falta de atmosfera na lua pode ser explicada usando o mesmo conceito. Como a atração gravitacional da lua é muito mais fraca, ela já perdeu quase toda a sua atmosfera.

Velocidades de Escape de Gases

Para escapar da gravidade da Terra, um objeto próximo ao topo da atmosfera a uma altitude de 100 km deve se afastar da Terra a 11,1 km/s. Essa velocidade ...

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The Kinetic Theory of Gases

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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.

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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

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

Why Lighter Gases Escape Earth First

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