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

La velocidad de escape es la velocidad mínima requerida para que un objeto no propulsado escape de la influencia de la fuerza gravitacional del objeto primario. La magnitud de la velocidad de escape de la Tierra es de 11,1 km/s.
¿Cuál es la temperatura a la que las moléculas de hidrógeno alcanzan la velocidad rms igual a la velocidad de escape de la Tierra?
De acuerdo con la teoría cinética de los gases, la energía cinética promedio de cualquier gas está relacionada con su temperatura. La masa de las moléculas de hidrógeno se puede calcular tomando la relación entre su masa molar y el número de Avogadro.
Ahora, reorganizando la ecuación para la energía cinética y sustituyendo las cantidades conocidas, se calcula la temperatura requerida para alcanzar la velocidad de escape.
La temperatura estimada es unos pocos órdenes de magnitud más alta que la temperatura a grandes altitudes de la atmósfera de la Tierra. Esto significa que las moléculas de hidrógeno no pueden escapar de la atmósfera terrestre.
Sin embargo, durante múltiples colisiones, moléculas de hidrógeno significativas alcanzan la velocidad de escape, lo que permite la pérdida de hidrógeno de la atmósfera de la Tierra.

<ol>
	<li>OpenStax. (2019). Física Universitaria Vol. 2. [Versión web]. Recuperado de la sección 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 Presión, Temperatura y Velocidad RMS - Física Universitaria Volumen 2 | OpenStax</a></li>
</ol>

velocidades de escape de los gases

Escape Velocities of Gases

Para escapar de la gravedad de la Tierra, un objeto cerca de la parte superior de la atmósfera a una altitud de 100 km debe alejarse de la Tierra a una velocidad de 11.1 km/s. Esta velocidad se llama velocidad de escape. La temperatura a la que las moléculas de gas alcanzan la velocidad cuadrática media, que es igual a la velocidad de escape, se puede estimar utilizando la ecuación para la energía cinética promedio de las moléculas de gas. Según la teoría cinética de los gases, la energía cinética promedio de las moléculas de gas es proporcional a su temperatura. Cuanto mayor sea la temperatura, mayor será la velocidad cuadrática media de las moléculas de gas. Para las moléculas de hidrógeno, la velocidad cuadrática media igual a la velocidad de escape se alcanza a una temperatura de 99.7 x 102 K. Esta temperatura es varios orden de magnitud más alta en comparación con la temperatura a una altitud de 100 km lejos de la superficie de la Tierra. A esas altitudes, la temperatura es aproximadamente de 250 K. Esto simplemente significa que la probabilidad de que las moléculas de hidrógeno escape de la atmósfera de la Tierra es insignificante. Sin embargo, por el contrario, muy pocas moléculas de hidrógeno quedan en la atmósfera de la Tierra. La pérdida de hidrógeno ocurre porque unas pocas moléculas tienen velocidades más altas que la velocidad de escape de la Tierra, incluso a temperaturas normales. La velocidad de una molécula de hidrógeno cambia de una colisión a la siguiente; por lo tanto, en cualquier instante, hay una pequeña pero finita posibilidad de que la velocidad de la molécula sea mayor que la velocidad de escape. La posibilidad es lo suficientemente alta como para que, a lo largo de la vida de la Tierra, casi todas las moléculas de hidrógeno en la atmósfera hayan alcanzado la velocidad de escape a altitudes elevadas y hayan escapado del tirón gravitacional de la Tierra. Sin embargo, las moléculas más pesadas, como el oxígeno, el nitrógeno y el agua, tienen velocidades cuadráticas medias más bajas, por lo que es mucho menos probable que alguna de ellas tenga velocidades mayores que la velocidad de escape. La probabilidad es tan pequeña que se requieren miles de millones de años para perder magnitudes significativas de moléculas más pesadas de la atmósfera. La falta de atmósfera en la luna se puede explicar utilizando el mismo concepto. Dado que la gravedad de la luna es mucho más débil, ha perdido casi toda su atmósfera.

Velocidades de escape de los gases

Para escapar de la gravedad de la Tierra, un objeto cerca de la parte superior de la atmósfera a una altitud de 100 km debe alejarse de la Tierra a 11,1 km/s. Esta velocidad ...

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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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