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

Скорость убегания — это минимальная скорость, необходимая для того, чтобы недвижимый объект мог уйти от влияния гравитационной силы основного объекта. Величина скорости убегания Земли составляет 11,1 км/с.
При какой температуре молекулы водорода достигают среднеквадратичной скорости, равной скорости убегания Земли?
Согласно кинетической теории газов, средняя кинетическая энергия любого газа связана с его температурой. Массу молекул водорода можно рассчитать, взяв отношение его молярной массы к числу Авогадро.
Теперь, переставив уравнение для кинетической энергии и подставив известные величины, вычисляется температура, необходимая для достижения скорости убегания.
Расчетная температура на несколько порядков выше, чем температура на больших высотах атмосферы Земли. Это означает, что молекулы водорода не могут покинуть атмосферу Земли.
Однако во время множественных столкновений значительные молекулы водорода достигают скорости убегания, что позволяет терять водород из атмосферы Земли.

<ol>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. Взято из раздела 2.2; стр. 83-84. <a href="https://openstax.org/books/university-physics-volume-2/pages/2-2-pressure-temperature-and-rms-speed">2.2 Давление, температура и среднеквадратичная скорость - Университетская физика Том 2 | OpenStax</a></li>
</ol>

Скорости побега газов.

Escape Velocities of Gases

Чтобы покинуть гравитацию Земли, объект, находящийся вблизи верхней границы атмосферы на высоте 100 км, должен удаляться от Земли со скоростью 11,1 км/с. Эта скорость называется скоростью побега. Температура, при которой молекулы газа достигают среднеквадратичной скорости, равной скорости побега, может быть оценена с помощью уравнения для средней кинетической энергии молекул газа. Согласно кинетической теории газов, средняя кинетическая энергия молекул газа пропорциональна его температуре. Чем выше температура, тем выше среднеквадратичная скорость молекул газа.

Для молекул водорода среднеквадратичная скорость, равная скорости побега, достигается при температуре 99.7 x 102 К. Эта температура на несколько порядков выше, чем температура на высоте 100 км от поверхности Земли. На таких высотах температура примерно 250 К. Это означает, что вероятность побега молекул водорода из атмосферы Земли ничтожно мала. Однако наоборот, в атмосфере Земли остаётся очень малое количество молекул водорода. Потери водорода происходят потому, что несколько молекул имеют скорости, превышающие скорость побега Земли, даже при нормальных температурах. Скорость молекулы водорода меняется от одного столкновения к другому; следовательно, в любой момент времени существует маленькая, но конечная вероятность того, что скорость молекулы превышает скорость побега. Вероятность достаточно высока для того, чтобы за время существования Земли почти все молекулы водорода в атмосфере достигли скорости побега на больших высотах и покинули гравитационное поле Земли.

Однако более тяжёлые молекулы, такие как кислород, азот и вода, имеют более низкие среднеквадратичные скорости, поэтому гораздо меньше вероятность того, что у них будет скорость, превышающая скорость побега. Вероятность настолько мала, что для значительной потери таких тяжёлых молекул из атмосферы требуется миллиарды лет. Отсутствие атмосферы на Луне можно объяснить с помощью этой же концепции. Поскольку гравитационное притяжение Луны гораздо слабее, ведь она потеряла практически всю атмосферу.

Чтобы избежать гравитации Земли, объект, находящийся в верхней части атмосферы на высоте 100 км, должен удаляться от Земли со скоростью 11,1 км/с. Эта скорость...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

The Kinetic Theory of Gases

Кинетическая теория газов

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

Heat capacity of gases depends on the gas type and the motion of its molecules. It is the amount of heat energy needed to raise the temperature of a unit mass of gas by one degree Celsius. This thermodynamic property is important in science and industry. To solve heat capacity problems, first identify the gas. A gas's molecular structure affects its heat capacity because the molecules have different degrees of freedom. These values can be found from tables or from empirical equations. Next,...

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

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Why Lighter Gases Escape Earth First

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