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Mean Free Path of Single-Species Gas Formula

GoMean Free Path using Number Density Formula

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The Mean Free Path of Molecule is the average distance an object will move between collisions. Check FAQs

λ = \frac{1}{\sqrt{2} \cdot n \cdot π \cdot d^{2}}

λ - Mean Free Path of Molecule?n - Number Density?d - Distance Between Two Bodies?π - Archimedes' constant?

Mean Free Path of Single-Species Gas Example

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Here is how the Mean Free Path of Single-Species Gas equation looks like with Values.

Here is how the Mean Free Path of Single-Species Gas equation looks like with Units.

Here is how the Mean Free Path of Single-Species Gas equation looks like.

0.0002 = \frac{1}{\sqrt{2} \cdot 9.8987 \cdot 3.1416 \cdot 12^{2}}

0.0002m = \frac{1}{\sqrt{2} \cdot 9.89871/m³ \cdot 3.1416 \cdot {12m}^{2}}

0.0002 = \frac{1}{\sqrt{2} \cdot 9.8987 \cdot 3.1416 \cdot 12^{2}}

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Mean Free Path of Single-Species Gas Solution

Follow our step by step solution on how to calculate Mean Free Path of Single-Species Gas?

FIRST Step Consider the formula

λ = \frac{1}{\sqrt{2} \cdot n \cdot π \cdot d^{2}}

Next Step Substitute values of Variables

∴

λ = \frac{1}{\sqrt{2} \cdot 9.89871/m³ \cdot π \cdot {12m}^{2}}

Next Step Substitute values of Constants

∴

λ = \frac{1}{\sqrt{2} \cdot 9.89871/m³ \cdot 3.1416 \cdot {12m}^{2}}

Next Step Prepare to Evaluate

∴

λ = \frac{1}{\sqrt{2} \cdot 9.8987 \cdot 3.1416 \cdot 12^{2}}

Next Step Evaluate

∴

λ = 0.000157904009907834m

LAST Step Rounding Answer

∴

λ = 0.0002m

Mean Free Path of Single-Species Gas Formula Elements

Variables

Constants

Functions

Mean Free Path of Molecule

The Mean Free Path of Molecule is the average distance an object will move between collisions.

Symbol: λ

Measurement: WavelengthUnit: m

Note: Value should be greater than 0.

Formulas to find Mean Free Path of Molecule

Number Density

Number Density is the moles of particles per unit volume.

Symbol: n

Measurement: Number DensityUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Number Density

Distance Between Two Bodies

Distance Between Two Bodies is the measurement of how far two bodies are placed.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance Between Two Bodies

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Mean Free Path of Molecule

Go Mean Free Path using Number Density

λ = \frac{1}{n \cdot π \cdot d^{2}}

Other formulas in Elements of Kinetic Theory category

Go Pressure using Kinetic Energy per Mole

p = \frac{2}{3} \cdot \frac{E' t}{V}

Go Volume of Gas

V = \frac{2}{3} \cdot \frac{E t}{p}

Go Kinetic Energy per Mole

E' t = \frac{3}{2} \cdot p \cdot V

Go Pressure using Molar Volume

p = \frac{2}{3} \cdot \frac{E' t}{V m}

How to Evaluate Mean Free Path of Single-Species Gas?

Mean Free Path of Single-Species Gas evaluator uses Mean Free Path of Molecule = 1/(sqrt(2)*Number Density*pi*Distance Between Two Bodies^2) to evaluate the Mean Free Path of Molecule, Mean Free Path of Single-Species Gas formula is defined as the average distance traveled by a molecule between successive collisions in a single-species gas, which is a fundamental concept in the kinetic theory of gases, describing the random motion of gas molecules and their interactions. Mean Free Path of Molecule is denoted by λ symbol.

How to evaluate Mean Free Path of Single-Species Gas using this online evaluator? To use this online evaluator for Mean Free Path of Single-Species Gas, enter Number Density (n) & Distance Between Two Bodies (d) and hit the calculate button.

FAQs on Mean Free Path of Single-Species Gas

What is the formula to find Mean Free Path of Single-Species Gas?

The formula of Mean Free Path of Single-Species Gas is expressed as Mean Free Path of Molecule = 1/(sqrt(2)*Number Density*pi*Distance Between Two Bodies^2). Here is an example- 0.000156 = 1/(sqrt(2)*9.89873*pi*12^2).

How to calculate Mean Free Path of Single-Species Gas?

With Number Density (n) & Distance Between Two Bodies (d) we can find Mean Free Path of Single-Species Gas using the formula - Mean Free Path of Molecule = 1/(sqrt(2)*Number Density*pi*Distance Between Two Bodies^2). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Mean Free Path of Molecule?

Here are the different ways to Calculate Mean Free Path of Molecule-

Mean Free Path of Molecule=1/(Number Density*pi*Distance Between Two Bodies^2)

Can the Mean Free Path of Single-Species Gas be negative?

No, the Mean Free Path of Single-Species Gas, measured in Wavelength cannot be negative.

Which unit is used to measure Mean Free Path of Single-Species Gas?

Mean Free Path of Single-Species Gas is usually measured using the Meter[m] for Wavelength. Megameter[m], Kilometer[m], Centimeter[m] are the few other units in which Mean Free Path of Single-Species Gas can be measured.

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