What is the kinetic theory of gases


Kinetic theory of gases:-The first material to be studied using modern scientific methods included gas, which was developed in the 1600s. It did not take long to acknowledge that the gases combined all the common bodily functions, suggesting that the gases could be described by a universal theory.
Dynamic molecular theory of gases.
There is a pattern that helps us understand the physical properties of gases at the molecular level.


Introduction of the kinetic theory of gases


The dynamic theory of gases states that gases are composed of particles in motion. Gas is constantly bombarded with pressure at any level. The higher the density of the gas, the greater the number and pressure of the collision between the molecules and the surface. So either the pressure increases when the volume of a certain amount of gas decreases, or when more gas is pumped into a vessel. When the temperature of a gas rises, the speed of the molecules increases, causing each collision to increase both the number and the speed. This increases the gas pressure as the temperature rises.

Maxwell (in 1860) explained some of the properties of the gas, explaining that gas molecules have flexible collisions, spend as much time as they really do in collisions, and have an insignificant fraction of the volume of the gas itself. Also, gravitational forces between molecules are considered to be non-existent.

It can be shown that the pressure for gas to occupy a volume V at P and in which each of the mass moving at an average speed is a molecule of M,

Also, the kinetic energy of a gas molecule is proportional to its thermodynamic temperature.

Kinetic theory of gases assumptions


The dynamic theory of gas hypotheses is as follows:

  1. All gases are made up of molecules that move in constant and permanent random directions.

  2. The separation between molecules is much greater than the number of molecules.

  3. When a gas sample is placed in a container, the molecules of the sample do not exert any force on the walls of the container during the collision.

  4. The collision between two molecules, and the distance between one molecule and the wall, is considered very small.

  5. All collisions between the molecule and the molecule and the wall are also considered flexible.

  6. All molecules in a particular gas sample obey Newton's laws of motion.

  7. If the gas sample is left for a long time, it eventually returns to a stable state. Molecular density and molecular distribution are independent of location, distance, and time.


kinetic theory of gases derivation


Consider a cubic box of length filled with a large meter of gas molecules, the velocity along the x-axis increases with vx so its velocity is MVX.

Gas molecules are hitting the walls. On wall 1, it collides with each other and takes advantage of it.

Similarly, molecules collide with wall 2, changing its speed, ie .mvx.

Thus, given by the change in speed

= p = mvx - (- mvx) = 2mvx —– (1)

After the collision, the molecule covers a distance of 2l before colliding again with wall 1.

Thus, the time taken is given by

Time = distance Default speed = 2lvx —- (2)

These constant collisions have a force, given by

Force = changenometinum change time = ΔpΔt —— (3)

Thus, changing the values ​​from the equations (1) and (2), we get

Force = 2mvx2lvx

Force (F) = mv2xl —— (4)

Constant collisions also put pressure on the wall.

Pressure = Force Area = FA

Pressure (P) = (MV2XL) L2
P = mv2xl3 (5)

We know that gas is made up of N molecules and moves in every possible direction. Thus, the collision of N with the number of gas molecules puts pressure on wall 1.

P = ml3 (v2x1 + v2x2 + v2x3 +… .. + v2xN)

= P = ml3 (Nv¯2x)

= P = mNv¯2xV —— (6)

Where,

v¯2x = v2x1 + v2x2 + v2x3 +… .. + v2xN is the average velocity (or component of velocity) of all gas molecules colliding with wall 1 in one direction.
And l3 = V

When we extend this equation to three dimensions, we get.

v2 = v2x + v2y + v2z

v¯2 = v¯2x + v¯2y + v¯2z

For a large number of gas molecules:

v¯2x = v¯2y = v¯2z

Or

v¯2 = 3v¯2x

⇒v¯2x = 13v¯2 -—- (7)

Converting equation (6) to alternative (6), we get

P = Nm (13v¯2) V

Upon resetting,

VPV = 13Nmv¯2 8 (8)

What is the importance of the dynamic theory of gases?


By knowing the temperature, we will get an honest idea of the typical K.E. of a gas molecule. It doesn't matter what gas you're considering. Unless and until it's a perfect gas.

By knowing the microscopic parameters of gases like pressure, volume, temperature, etc., microscopic parameters like a moment, speed, internal energy, K.E., thermal energy, etc., and the other way around are often accurately calculated.