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

脱出速度は、推進されていない物体が一次物体の重力の影響から脱出するために必要な最小速度です。地球の脱出速度の大きさは11.1km/sです。
水素分子が地球の脱出速度に等しいrms速度に達する温度はどれくらいですか?
ガスの運動理論によれば、あらゆるガスの平均運動エネルギーはその温度に関連しています。水素分子の質量は、その分子量とアボガドロ数との比を取ることによって計算できます。
ここで、運動エネルギーの方程式を並べ替え、既知の量を代入すると、脱出速度を達成するために必要な温度が計算されます。
推定温度は、地球の大気の高高度の温度よりも数桁高いです。これは、水素分子が地球の大気から逃げることができないことを意味します。
しかし、複数回の衝突時には、かなりの水素分子が脱出速度に達し、地球の大気から水素が失われる可能性があります。

<ol>
	<li>OpenStaxです。(2019). 大学物理学 Vol.2.【Web版】。セクション2.2から取得。83-84ページ<a href="https://openstax.org/books/university-physics-volume-2/pages/2-2-pressure-temperature-and-rms-speed">2.2 圧力、温度、RMS速度 - University Physics Volume 2 |OpenStaxの</a></li>
</ol>

ガスの脱出速度

Escape Velocities of Gases

地球の重力から逃れるには、高度 100 km の大気圏の上部付近にある物体は、秒速 11.1 km で地球から遠ざかる必要があります。 この速度を脱出速度といいます。 気体分子が実効速度（脱出速度に等しい）に達する温度は、気体分子の平均運動エネルギーの方程式を使用して推定できます。 気体の運動理論によれば、気体分子の平均運動エネルギーはその温度に比例します。 温度が高いほど、ガス分子の実効速度は高くなります。

水素分子の場合、脱出速度に等しい rms 速度は 99.7 x 102 K の温度で達成されます。この温度は高度での温度と比較して数桁高いです。 地表から100キロメートル離れたところにあります。 このような高度では、温度はおよそ 250 K です。これは単に、水素分子が地球の大気から逃げる可能性が無視できることを意味します。 しかし、それどころか、地球の大気中には水素分子はほとんど残っていません。 水素の損失は、常温でも少数の分子が地球の脱出速度よりも速い速度を示すために発生します。 水素分子の速度は衝突ごとに変化します。 したがって、いかなる瞬間においても、分子の速度が脱出速度よりも速くなる可能性は小さいですが有限です。 その可能性は十分に高く、地球の生涯にわたって、大気中のほぼすべての水素分子が高高度で脱出速度に達し、地球の重力から逃れる可能性があります。

ただし、酸素、窒素、水などのより重い分子は実効速度が低いため、脱出速度を超える速度を持つ分子が存在する可能性ははるかに低くなります。 可能性は非常に小さいため、大気中からかなりの量の重い分子が失われるには何十億年もかかります。 月の大気の欠如も、同じ概念を使用して説明できます。 月の引力ははるかに弱いため、大気のほぼ全体が失われています。

地球の重力から逃れるには、高度100kmの大気頂上付近にある物体は、地球から秒速11.1kmで移動する必要があります。この速度...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

The Kinetic Theory of Gases

気体分子運動論

KEY TERMS AND CONCEPTS

主要用語と概念

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

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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

physics

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Why Lighter Gases Escape Earth First

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