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

The escape velocity is the minimum velocity required for a non-propelled object to escape from the influence of the gravitational force of the primary object. The magnitude of the escape velocity of the Earth is 11.1 km/s.
What is the temperature at which hydrogen molecules attain the rms speed equal to the escape velocity of the Earth?
According to the kinetic theory of gases, the average kinetic energy of any gas is related to its temperature. The mass of hydrogen molecules can be calculated by taking the ratio of its molar mass to Avogadro&#39;s number.
Now, rearranging the equation for kinetic energy and substituting the known quantities, the temperature required to attain the escape velocity is calculated.
The estimated temperature is a few orders of magnitude higher than the temperature at high altitudes of Earth&#39;s atmosphere. This means the hydrogen molecules cannot escape from the Earth&#39;s atmosphere.
However, during multiple collisions, significant hydrogen molecules attain the escape velocity allowing the loss of hydrogen from Earth&#39;s atmosphere.

escape velocities of gases

Escape Velocities of Gases

To escape the Earth&#39;s gravity, an object near the top of the atmosphere at an altitude of 100 km must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. The temperature at which gas molecules attain the rms speed, which is equal to the escape velocity, can be estimated by using the equation for the average kinetic energy of the gas molecules. According to the kinetic theory of gas, the average kinetic energy of the gas molecules is proportional to its temperature. The higher the temperature, the higher the rms speed of the gas molecules.
For hydrogen molecules, the rms speed equal to the escape velocity is attained at a temperature of 99.7 x 102 K. This temperature is a few orders of magnitude higher compared to the temperature at an altitude of 100 km away from the Earth&#39;s surface. At such altitudes, the temperature is roughly 250 K. This simply means that the probability of hydrogen molecules escaping the Earth&#39;s atmosphere is negligible. However, on the contrary, very few hydrogen molecules are left in the Earth&#39;s atmosphere. The hydrogen loss occurs because a few molecules have speeds higher than the Earth&#39;s escape velocity, even at normal temperatures. The speed of a hydrogen molecule changes from one collision to the next; hence, at any instant, there is a small but finite chance that the molecule&#39;s speed is greater than the escape velocity. The chance is high enough that over the lifetime of Earth, almost all the hydrogen molecules in the atmosphere have reached the escape velocity at high altitudes and escaped from the Earth&#39;s gravitational pull.
However, heavier molecules, such as oxygen, nitrogen, and water, have lower rms speeds, so it is much less likely that any of them will have speeds greater than the escape velocity. The likelihood is so small that billions of years are required to lose significant amounts of heavier molecules from the atmosphere. The moon&#39;s lack of atmosphere can be explained using the same concept. Since the Moon&#39;s gravitational pull is much weaker, it has lost almost its entire atmosphere.

To escape the Earth&#39;s gravity, an object near the top of the atmosphere at an altitude of 100 km must travel away from Earth at 11.1 km/s. This speed ...

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JoVE Core

Physics

Unit 1

The Kinetic Theory of Gases

KEY TERMS AND CONCEPTS

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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