Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. This is possible as the interatomic forces which are short range forces that are important for solids and liquids can be neglected for gases. This theory was developed by Maxwell, Boltzman and others.
This theory is based on certain assumptions. They are
* Every gas consists of extremely small particles known as molecules. These are identical but are different from other gases.
* The molecules are identical, spherical, rigid and perfectly elastic point masses.
* Molecules of a gas keep on moving randomly in all possible directions with all possible velocities. The speed of gas molecules lie between zero and infinity.
* Gas molecules keep on colliding among themselves as well as with the walls of containing vessel. The collisions are perfectly elastic.
* Molecule moves along a straight line between two successive collisions and the average straight distance covered between two successive collisions is called mean free path.
* Molecules constantly collide with walls of container due to which their momentum changes. The change in momentum is transferred to the walls of container.
* Density of a gas is constant at all points in the container.
Pressure of an ideal gas:
Consider an ideal gas enclosed in a cube of side l. The sides of the cube are parallel to the co-ordinate axes. A molecule of mass 'm' moving with velocity . This velocity can be resolved into components x, y and z along X, Y and Z axes respectively. A molecule with velocity (vx, vy, vz) hits the planar wall parallel to YZ - plane of area A (= l2). Since the collision is elastic the molecule rebounds with same velocity, its Y and Z components do not change and the X - component reverses sign. Initial momentum of the molecule along X - axis is mvx. Final momentum of molecule along X - axis is -mvx. Change in momentum of molecule along X - axis is -2mvx. The time interval between two successive collisions of a molecule with same wall is
Kinetic interpretation of Temperature: 
i.e., the pressure exerted by an ideal gas is numerically equal to the two third of the mean kinetic energy of translation per unit volume of the gas.
But PV = NkT 
... Average K.E. of molecule is proportional to absolute temperature of the gas.
Root Mean Square (rms) velocity:
The square root of mean of squares of the speeds of different molecules is called root mean square velocity. 
rms speed of gas do not depends on pressure of the gas. At T = 0, vrms = 0, the rms speed of molecules of a gas is zero at 0°K. This temperature is called absolute temperature & absolute zero.
Most Probable Speed: The speed possessed by maximum number of molecules in a gas at constant temperature is called most probable speed.
Average Speed: It is the arithmetic mean of the speeds of molecules in a gas at given temperature.
Law of equipartition energy: A molecule free to move in space needs three coordinates to specify its location. If it is constrained to move along a line, it needs one co-ordinate to locate it, if it is constrained to move in a plane it needs two co-ordinates. This can also be expressed in terms of degrees of freedom.
The term degrees of freedom of a system refers to the possible independent motions a system can have. Motion of a body as a whole from one point to other is called translational motion. Thus a molecule free to move in space has three translational degrees of freedom. Thes
In case of triatomic gas or polyatomic gas (molecule) can rotate about any of three co-ordinate axes. Hence it has 6 degrees of freedom, 3- translational and 3 - rotational. The atoms within the molecules may also vibrate with respect to each other. In such case it may have additional degrees of freedom due to vibration.
Now
Specific heat in terms of degrees of freedom:
Cv: From kinetic theory of gases the internal energy
Mean free path: Molecules in a gas have rather large speeds of the order of speed of sound. The top of a cloud of smoke holds together for hours. This happens because molecules in a gas have a finite, small size. So they are bound to undergo collisions. As a result they cannot move straight unhindered; their paths keep getting instantly deflected.
Suppose the molecules of a gas are spheres of diameter 'd', the average speed of molecule is < v >. Molecules suffer collisions with any molecule that comes within a distance 'd' between centres. In time Δt, it sweeps a volume πd2 < v > Δt. If n no. of molecules are there per unit volume, the molecule suffers nπd2 < v < Δt. The time between two successive collisions is
