Difference Between Mean Free Path and Pressure

Key Difference – Mean Free Path vs Pressure
 

Mean free path is the average distance travelled by a moving molecule while colliding with other molecules. Hence, it is measured by units of measurement of length. The mean free path is determined using the average speed of a molecule, and the collision frequency since determining the mean free path using the distances is difficult. Pressure is a scientific term that is often used. It is the perpendicular force applied on a unit surface area. The key difference between mean free path and pressure is that mean free path is measured as a distance in meters whereas pressure is measured by the SI unit Pascals (Pa).

CONTENTS

1. Overview and Key Difference
2. What is Mean Free Path
3. What is Pressure
4. Side by Side Comparison – Mean Free Path vs Pressure in Tabular Form
6. Summary

What is Mean Free Path?

The mean free path is the average distance travelled by a moving particle (an atom, molecule or ion) between collisions (successive impacts). These collisions modify the direction or energy of moving particles. This term is called mean free path because it is calculated as an average value. The mean free path can be estimated using kinetic theory. The kinetic theory states that gas molecules are in constant random motion with frequent collisions with each other. The mean free path is denoted by the symbol “λ”. Let us consider an example to understand what mean free path is.

Figure 1: Motion of a gas molecule with collisions between the gas molecule and the wall of the container.

Mean Free Path Calculation

The mean free path of the gas molecule in above image is given as below.

λ    =   (D1 + D2 + D3 + D4) /4

However, this type of calculation is not possible because the distances between each collision cannot be determined easily. Hence, the mean free path is calculated as follows.

λ    =    {c} / Z

Here, {c} is the average speed of a gas molecule and Z is the collision frequency. The collision frequency is the rate at which two molecules collide with each other. Therefore, it is equal to 1/t (t is the average time between collisions). Then the above equation can be rearranged as follows.

λ    =    {c} / (1/t)

λ    =    {c} t

What is Pressure?

Pressure is a scientific term used to name the force applied perpendicular to a unit surface area. When a fluid is considered, the pressure is the stress at a point within a fluid. The SI unit of measuring the pressure is Pascal (Pa). The pressure is denoted by the symbol “P”. However, there are some several common units used to measure the pressure. Ex: N/m² (Newton per square meter), psi (the pound-force per square inch), atm (atmosphere), 1/760 of atm is named as one torr.

Figure 2: Pressure is the perpendicular force applied on a surface divided by the surface area on which the force is exerted.

Equation for Calculation of Pressure

The pressure can be calculated using the following equation:

P = – (F/A)

Where p is the pressure, F is the magnitude of the force applies on an area of A. There are several types of pressure.

1. Fluid pressure – the compressive force on a point within a fluid.
2. Explosion pressure – the pressure resulted by ignition of explosive gases.
3. Negative pressure – there are certain conditions where the pressure becomes negative. Ex: when the intermolecular forces between fluid molecules exceed the repulsive forces (that is created due to thermal motion).
4. Pressure of an ideal gas – the pressure of an ideal gas is calculated using P=nRT/V (in which P is the pressure, n is the amount of substance, R is the universal gas constant, V is the volume and T is the temperature of the gas).
5. Vapor pressure – the pressure of vapor that is in touch with its liquid phase in a closed thermodynamic system.

What is the Difference Between Mean Free Path and Pressure?

Summary – Mean Free Path vs Pressure

Mean free path is the average of distances travelled by a molecule between collisions during motion. Pressure is the force applied on a unit surface area in a perpendicular direction. The key difference between mean free path and pressure is that mean free path is measured as a distance in meters whereas pressure is measured by the SI unit Pascals (Pa).

Reference:

1. “Mean Free Path.” Chemistry LibreTexts, Libretexts, 21 July 2016, Available here.
2. “Mean free path.” Wikipedia, Wikimedia Foundation, 28 Feb. 2018, Available here.
3. “Mean Free Path.” Mean Free Path, Molecular Collisions, Available here.

Image Courtesy:

1.”Pressure force area” By Klaus-Dieter Keller – Own work (CC BY-SA 3.0) via Commons Wikimedia

Related posts:

Difference Between Force and Pressure Difference Between Vapor Pressure and Partial Pressure Difference Between Hydrostatic Pressure and Osmotic Pressure Difference Between Order of Reaction and Molecularity Difference Between Thermal Decomposition and Thermal Dissociation