IIT JEE and NEET Physics @ Venkats Academy IIT-JEE and NEET Physics

The purpose of the Kinetic theory of the gases is to link to the macroscopic properties of the gases like pressure volume,temperature with the macroscopic properties of the gas molecules like displacement,velocity, momentum, force and kinetic energy.

To apply the connect theory of the gases to the molecules we shall make some assumptions.

1. We shall assume that the size of the molecule is very small and when compared with the volume of the gas occupied the volume of the gas molecules occupied is negligible.

2. The gas molecules are tiny in size , spherical in shape , neutral with respect to charge and all are identical.

3. The molecules moves in all directions randomly with all possible speeds.

4. The collision of the gas molecules is an elastic. That means during the collision both momentum and kinetic energy are conserved. There is no wastage of energy in the format of sound light and heat.

Mean free path:

The average distance molecule can travel without colliding the neighboring molecules is called as mean free path.When the molecule starts its journey, its motion is so random under regular that the we cannot predict what is going to be its path is.

In between any of the two collisions, the molecule travel some distance and by measuring this total distances and by dividing it with the number of the collisions we can calculate the value of the mean free path.

The gas which obeys all gas laws at all temperatures and pressures is called an ideal gas. In reality no gas is actually Ideal and all the existing gases are called real gases.While explaining kinetic theory of the gases, anyway we assume that the gas is Ideal.

Practically real gas obeys all gas laws only at high temperatures and low pressures.

Expression of the pressure of an ideal gas:

Being the gas molecules are having collisions among themselves and with the walls of the container, they are going to exert some pressure and here we are going to calculate that pressure. Let us consider a container who is having cube shape. Let the side of the cube is L and a gas molecule of mass m is moving in parallel to YZ plane along the x-axis.

As the collision is elastic the molecule will come back with the same velocity.Thus we can calculate the change of the momentem with respect to time which leads the calculation of the force. The derivation for the pressure is made are shown below.

This can be further continued by writing all the forces and then further writing equation for the pressure as defined as the force per unit area as shown further.

The expression for the pressure of a gas molecule can be expressed in terms of kinetic energy of the gas molecule also. Here RMS velocity of the gas molecule can be expressed as the root mean square velocity of the gas molecule. Basing the ideal gas equation even we can measure the impact of the temperature here. The temperature at which the RMS velocity of gas molecule becomes zero is called a absolute zero temperature and that is taken as a reference to define Kelvin scale.

We can further find a relation between temperature of the gas and the RMS velocity of the gas molecule as shown below.We can also define a particular temparatue at which RMS velocity of gas molecule become zero called absolute temperature.

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Distance and displacement comparison

The entire physics subject can be broadly divided into two categories.They are classical physics in modern physics. For the science to be called as a classical physics, it shall be developed at the beginning of science.The classical physics deals with the macroscopic bodies that what we are able to see. In the other way classical physics is a macroscopic physics that we can directly experience up to some extent. If a time deadline has to be kept,it is developed before 1900 A.C. Newton is being treated as the father of the classical mechanics. His laws of motion has given a crystal clear clarity that how the body moves which are macroscopic in nature when force is applied.

Modern physics deals with the microscopic bodies like electrons and protons.It is obvious that we cannot see them therefore we have to depend on experimental results to draw the conclusions.

Translatory motion is one of the basic topics of classical mechanics. It basically deals with the bodies that are moving along a straight line.The Newton laws are actually applied for a elementary part of a body called particle. A particle is a body of negligible dimensions. As the body is a combination of so many particles the rules that are developed for the particle can be applied for the body also.

The branch of physics which deals with the motion of the body without worrying about the forces acting on it could be called as kinematics. In the other way this emotion of your body along only one dimension.To study this one-dimensional motion we need to know some basic terms.

The first set of the fundamental terms that we are going to define here are rest and motion.These words are in fact relative. We are saying these words with respect to the earth because we are on the earth.

The particle who doesn't change its position with respect to time and surroundings is said to be in the state of rest. Obviously the particle who is changing its position continuously with respect to the time and surroundings is said to be in the state of motion.

Next we would like to define a set of terms called distance and displacement.Distances the actual path followed by a body between its initial and final positions,where as the displacement is the shortest possible distance between initial and final positions in the specified direction.

Between any two specified points there may be different distances because there may be different paths but the displacement is going to be only one as it is going to be the shortest possible distance between the two specified points.It is quite possible that a distance can be greater than displacement is the path chosen could be greater than the shortest possible path. But displacement will never be greater than that of distance and get the best displacement is equal to distance.

Distances are scalar quantity which has only magnitude. Displacement is a vector quantity which has both magnitude and direction.As it is explained in the previous lessons some physical quantities demands both magnitude and direction to understand completely and the physical quantities are being called as vectors.

Now let us consider solving a problem on distance and displacement. Let us consider a body in circular motion of radius r.Find the distance and displacement covered by your body when it covers one fourth of the circular motion.

Let us consider solving another problem where a circular body of radius R is moving on a smooth horizontal surface.Find its displacement when half of circular motion is completed ?

The problem is solved as shown and here displacement is simple shortest possible distance between initial and final positions.