Kinetic theory of gases

The Kinetic Theory of Gases claims explain in detail the behavior of these fluids, by theoretical procedures based on a postulated description of a gas and some assumptions. This theory was first proposed by Bernoulli in 1738, and later expanded and improved by Clausius, Maxwell, Boltzmann, van der Waals, and Jeans.

Postulates of the Kinetic Theory of Gases

The fundamental postulates of this theory are:

1.- It is considered that Gases are made up of tiny discrete particles calledmolecules of equal mass and size in the same gas, but different for different gases.

2.- The molecules of a container are in chaotic movement incessantly, during which they collide with each other or with the walls of the container where they are.

3.- The bombardment of the vessel walls causes a pressure, that is, a force per unit area, average of the Collisions of the molecules.

4.- The collisions of molecules are elasticIn other words, as long as the pressure of the gas in a container does not vary over time at any temperature and pressure, there is no loss of energy due to friction.

5.- The Absolute temperature is a quantity proportional to the Average Kinetic Energy of all the molecules in a system.

6.- At relatively low pressures, the average distance between the molecules is large compared to their diameters, and hence the attractive forces, which depend on molecular separation, are considered negligible.

7.- Finally, as the molecules are small compared to the distance between them, their volume is considered negligible in relation to the total covered.

By ignoring the size of the molecules and their interaction, as shown by postulates 6 and 7, this theoretical treatise is limited to ideal gases.

A mathematical analysis of this gas concept leads us to fundamental conclusions directly verifiable by experience.

Physical Explanation of the Kinetic Theory of Gases

Suppose a cubic container filled with n 'molecules of gas, all equal, and with the same mass and velocity, m and u respectively. It is possible to decompose the velocity u into three components along the x, y and z axes.

If we designate these three components u_x, or_Y, or_z, then:

or² = u_x² + u_Y² + u_z²

where u² is the root mean square velocity. Now we associate to each of these components a single molecule of mass m capable of moving independently in any of the corresponding x, y, z directions.

The final effect of these independent movements is obtained by combining the speeds according to the equation.

Now suppose that the molecule moves in the x direction to the right with the velocity u_x. It will collide with the plane and z with the moment mu_x, and since the collision is elastic, it will bounce with a velocity -u_x and the momentum -mu_x.

Consequently, the Variation of the Amount of Motion, or Momentum, per molecule and collision in the x direction is mu_x - (-mu_x) = 2mu_x.

Before you can hit the same wall again, you must walk back and forth to the one in front of you. In doing so, it travels a distance 2l, where l is the edge length of the cube. From this we deduce that the number of collisions with the right wall of the molecule in one second will be u_x/ 2l, so the change in moment per second and molecule will be worth:

(2mu_x)(or_x/ 2l) = mu_x²/ l

The same variation occurs for the same molecule in the yz plane so that the total change in the quantity of motion per molecule and second in the x direction, is twice the amount indicated in the latter equation. So it is explained:

Change of Moment / second / molecule, in the direction x = 2 (mu_x²/l)

Examples of Gases studied by the Kinetic Theory

1. Hydrogen H
2. Helium He
3. Neon Ne
4. Refrigerant 134a
5. Ammonia NH₃
6. Carbon Dioxide CO₂
7. Carbon Monoxide CO
8. Air
9. Nitrogen N
10. Oxygen O