Name: gas pressure and molecular motion
Uploaded: 2023-04-30T12:30:41.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Louisiana Student Standards for Science

High School

Chemistry

Matter And Its Interactions

HS-PS1-4

Molecular Kinetic Energy

Weźmy pod uwagę gaz w pojemniku; przypadkowy ruch cząsteczek powoduje kilka zderzeń ze ściankami.
Podczas zderzeń każda cząsteczka wywiera siłę na ścianki pojemnika, która jest źródłem ciśnienia wywieranego przez gaz.
Jeśli wszystkie cząsteczki gazu mają tę samą wielkość prędkości, oddziaływanie ze ścianą w kierunku x w krótkich odstępach czasu powoduje zmianę składowej x prędkości i pędu.
Jeśli liczba cząsteczek na jednostkę objętości pozostaje jednolita, można określić liczbę zderzeń dla określonego obszaru i zmianę całkowitego pędu w krótkim przedziale.
Stosując drugie prawo Newtona, ciśnienie wywierane przez gaz zależy od masy, prędkości i liczby cząsteczek na objętość cząsteczki.
Biorąc pod uwagę stan izotropowy, średnia prędkość cząsteczki gazu jest związana ze składowymi prędkości i jest równa trzykrotnej prędkości składnika.
Podstawiając i porównując z równaniem gazu doskonałego, określa się średnią translacyjną energię kinetyczną n moli gazu.

Ten tekst został zaadaptowany z <a href="https://openstax.org/books/university-physics-volume-2/pages/2-1-molecular-model-of-an-ideal-gas">Openstax, University Physics Volume 2, Section 2.2: Pressure, Temperature, and RMS Speed. </a>

molekularna energia kinetyczna

Słowo „gaz” pochodzi od flamandzkiego słowa oznaczającego „chaos”; po raz pierwszy użyty do opisu oparów przez chemika J. B. van Helmonta. Rozważmy pojemnik wypełniony gazem, w którym cząsteczki poruszają się w sposób ciągły i losowy. Podczas zderzeń składowa prędkości równoległa do ściany pozostaje niezmieniona, a składowa prostopadła do ściany zmienia kierunek, ale nie zmienia wielkości. Jeśli prędkość cząsteczki zmienia się w kierunku x, wówczas zmienia się jej pęd. W krótkim czasie zderzenia każda cząsteczka wywiera siłę na ścianki pojemnika, co jest źródłem ciśnienia wywieranego przez gaz. Wywieraną siłę można wyrazić w postaci prędkości, gdzie całkowita prędkość do kwadratu jest sumą kwadratów jej składowych (x-, y- i z-kierunki). Ponadto, zastępując wartości i porównując je z równaniem gazu doskonałego, można wyznaczyć średnią energię kinetyczną translacji n moli gazu doskonałego. Uzyskany wynik pokazuje, że średnia energia kinetyczna translacji jest wprost proporcjonalna do temperatury bezwzględnej.

Średnia prędkość kwadratowa cząstek w gazie jest definiowana jako pierwiastek kwadratowy średniej prędkości do kwadratu cząsteczek w gazie, natomiast średnia przebyta odległość i czas między zderzeniami nazywana jest średnią swobodną drogą, a oznaczają odpowiednio czas wolny. Średnia swobodna droga jest odwrotnie proporcjonalna do liczby cząsteczek na jednostkę objętości, a także odwrotnie proporcjonalna do pola przekroju poprzecznego cząsteczki; im większe cząsteczki lub im większa liczba cząsteczek, tym krótsza średnia odległość między zderzeniami.

Molekularna energia kinetyczna

Słowo "gaz" pochodzi od flamandzkiego słowa oznaczającego "chaos", po raz pierwszy użytego do opisania oparów przez chemika J. B. van Helmonta. Rozważać...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

The Kinetic Theory of Gases

Kinetyczna teoria gazów

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 momentum changes. During the short collision, the molecule exerts a force on the wall. That force is the source of gas pressure.

The force from many collisions can be written in terms of velocity. The total speed squared equals the sum of the squares of the x-, y-, and z-direction components. By substituting these values and comparing the result with the ideal gas equation, the average translational kinetic energy of n moles of an ideal gas can be found. This average translational kinetic energy is directly proportional to absolute temperature.

The root-mean-square speed is the square root of the average of the velocity squared for gas molecules. Gas motion also includes mean free path and mean free time. Mean free path is the average distance a molecule travels between collisions, and mean free time is the average time between collisions. The mean free path becomes shorter when there are more molecules per unit volume or when molecule cross-sectional area is larger.

Gas Pressure and Molecular Motion

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 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

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.

key terms and concepts

Explore how gas pressure comes from molecular collisions, how ideal gas temperature links to kinetic energy, and what mean free path and rms speed mean.

Gas Pressure and Molecular Motion | JoVE K12

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JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

HS-PS1-5

Arizona Science Standards

Physical Science

HS+C.P1

HS+C.P1U1.3

Next Generation Science Standards

Energy

HS-PS3-1

HS-PS3-2

Florida Department of Education

SC.912.P.10

SC.912.P.10.5

SC.912.P.12

SC.912.P.12.10

SC.912.P.12.11

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HS-PS1-3

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Gas Pressure and Molecular Motion

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