Name: gas collisions: path length and time
Uploaded: 2025-05-22T09:05:59.000Z
Duration: 1 min 22 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.12

SC.912.P.12.10

Mean free path and Mean free time

Silindirik bir hacim V'de v hızıyla rastgele hareket eden r yarıçaplı N gaz molekülünü düşünün. Bir molekül başka bir molekülle çarpıştığında, merkezleri arasındaki mesafe 2r'dir.
Yarıçapı 2r olan, ekseni molekülün hızına paralel olan bir silindir hayal edin. Molekül küçük bir zaman aralığı boyunca hareket ettiğinde ve silindirin içinde çarpıştığında, birim zamandaki çarpışma sayısı belirlenebilir.
Ortalama bağıl hız denklemi kullanılarak, birim zamandaki tüm hareketli moleküller için çarpışmalar belirlenebilir.
Denklemin tersi, ortalama boş zaman olarak bilinen çarpışmalar arasındaki ortalama süreyi verir.
Bu arada, bir gaz molekülünün ortalama serbest yolu, molekülün hızının ve çarpışmalar arasındaki ortalama sürenin ürünüdür. Terimleri değiştirerek, birim hacim başına molekül sayısı ve molekülün kesit alanı ile ters orantılı olan ortalama serbest yol belirlenebilir.
İdeal gaz denklemini hatırlayarak ve terimleri değiştirerek, gazın makroskopik özellikleri elde edilebilir.

<ol>
	<li>Genç, H.D ve Freedman, R.A. (2012). Modern Fizik ile Üniversite Fiziği. San Francisco, Kaliforniya: Pearson. Sayfa 630</li>
	<li>Stax'ı açın. (2019). Üniversite Fiziği Cilt 1. [Web sürümü]. <a href="https://openstax.org/books/college-physics-2e/pages/13-4-kinetic-theory-atomic-and-molecular-explanation-of-pressure-and-temperature" adresinden alındı>https://openstax.org/books/college-physics-2e/pages/13-4-kinetic-theory-atomic-and-molecular-explanation-of-pressure-and-temperature</a></li>
</ol>

ortalama serbest yol ve ortalama serbest zaman

Bir silindirdeki gaz moleküllerini düşünelim. Birbirleriyle çarpışıp hız ve yön değiştirdikleri rastgele bir hareketle hareket ederler. Tüm çarpışmalar arasındaki yol uzunluklarının ortalaması "ortalama serbest yol" olarak bilinir.

<img alt="Equation1" src="/files/ftp_upload/14168/14168_Equation_1_new.svg" style="text-align: center; height: 40px;" />

Ortalama serbest yol, moleküllerin yoğunluğuyla ters orantılı olarak değişir çünkü bir hacim içinde daha fazla molekül olduğunda birbirleriyle çarpışma şansı daha fazla olur ve bu da ortalama serbest yolu azaltır. Ayrıca, ortalama serbest yol, moleküllerin çapıyla ters ilişkilidir çünkü nokta kütleleri olsalardı hiçbir zaman çarpışmazlardı. Bu nedenle, daha büyük moleküller daha kısa bir ortalama serbest yola sahiptir.

Sabit basınç altında sıcaklık arttıkça gaz genişler; böylece moleküller arasındaki ortalama mesafe ve ortalama serbest yol artar. Ancak sabit sıcaklıkta basınç arttırıldığında gaz sıkışır, bu da ortalama serbest yolun azalmasına neden olur. Ortalama serbest yol, ortalama hızın ve ortalama serbest zamanın çarpımı olarak tanımlanabilir, burada ortalama serbest zaman çarpışmalar arasındaki ortalama zaman olarak tanımlanır.

273 K sıcaklıkta ve 1 atm basınçta rastgele hareket eden 9.9 g/mol kütlesi olan argon atomlarını düşünelim. Bir argon atomunun yarıçapını 1.70 × 10-10m alarak, argon atomlarının ortalama serbest zamanını belirleyelim.

Sorunu çözmek için önce bilinen ve bilinmeyen miktarları belirleyin ve bunları SI birimlerine dönüştürün.

İkincisi, gaz molekülleri için RMS hız denklemini hatırlayın. Değerleri yerine koyarak RMS hızı aşağıdaki gibi belirlenebilir:

<img alt="Equation2" src="/files/ftp_upload/14168/14168_Equation_2_new.svg" style="text-align: center; height: 45px;" />

Son olarak, ortalama serbest zaman denklemini hatırlayın. Değerleri yerine koyarak ortalama serbest zaman aşağıdaki gibi belirlenebilir.

<img alt="Equation3" src="/files/ftp_upload/14168/14168_Equation_3_new.svg" style="text-align: center; height: 40px;" />

Ortalama serbest yol ve ortalama serbest zaman

Bir silindirdeki gaz moleküllerini düşünün. Birbirleriyle çarpışırken ve hız ve yön değiştirirken rastgele bir hareketle hareket ederler. Hepsinin ortalaması ...

Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

The Kinetic Theory of Gases

Gazların Kinetik Teorisi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 molecules have a shorter mean free path, while point masses would never collide.

Temperature and pressure also affect the mean free path. When temperature increases at constant pressure, a gas expands. The average distance between molecules increases, and the mean free path increases too. When pressure increases at constant temperature, the gas compresses. That reduces the mean free path.

The mean free path can also be written as the product of average speed and mean free time. Mean free time is the average time between collisions. A sample problem uses argon atoms with a molar mass of 39.9 g/mol at 273 K and 1 atm. The radius of an argon atom is taken as 1.70 × 10 -10 m. To find the mean free time, first identify the known and unknown values and convert them to SI units. Then use the RMS speed equation for gas molecules. After that, substitute the values into the mean free time equation to calculate the result.

Gas collisions: path length and time

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

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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...

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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

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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

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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 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

Learn how gas molecule collisions determine mean free path and mean free time, and see how density, size, temperature, and pressure affect them in argon.

Gas collisions: path length and time | JoVE K12

physics

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A. Motion can be measured and described qualitatively and quantitatively. Net forces create a change in motion. When objects travel at speeds comparable to the speed of light, Einstein's special theory of relativity applies.

B. Momentum is conserved under well-defined conditions. A change in momentum occurs when a net force is applied to an object over a time interval.

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Gas collisions: path length and time

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