What are the basic postulates of kinetic theory of gases?

The basic postulates of kinetic theory of gases are:

(i) All gases consist of atoms or molecules. The atoms or molecules of one gas are all similar to one another and different from the molecules of the other gas.

(ii) Molecules of a gas are in random motion.

(iii)The volume occupied by gas molecules is negligibly small as compared to volume of the container.

(iv) Molecules collide with each other. The collisions are elastic and instantaneous.

(v) Between the two consecutive collisions, the path followed by molecules is straight line.

(vi) Gas molecules do not exert any force of attraction or repulsion upon each other. 

Avogadro law states that under similar physical conditions of temperature and pressure, equal volume of all the gases contains equal number of molecules. 

Let P be the pressure, V be the volume and T be the absolute temperature. 

Let us consider two gases having same P, V and T. Let one gas contains n₁ molecules, each of mass m₁ and second gas contains n₂ molecules each of mass m₂. Let v₁, and v₂ be the r.m.s. velocities of two gases.

Now, According to kinetic theory of gases, pressure of an ideal gas is given by 

$$\begin{gathered} \mathrm{P} = \frac{1}{3}{\mathrm{\rho v}}^2 = \frac{1}{3}\frac{\mathrm{M}}{\mathrm{V}}{\mathrm{v}}^2 = \frac{1}{3} \frac{\mathrm{nm}}{\mathrm{V}}{\mathrm{v}}^2 \\ \mathrm{For} \mathrm{gas} \mathrm{having} \mathrm{mass} {\mathrm{m}}_1, \\ \mathrm{P}\hspace{0.17em}= \frac{1}{3} \frac{{\mathrm{n}}_1{\mathrm{m}}_1}{\mathrm{V}} {{\mathrm{v}}_1}^2 ... \left(1\right) \\ \mathrm{For} \mathrm{gas} \mathrm{having} \mathrm{mass} {\mathrm{m}}_{2,} \\ \mathrm{P}\hspace{0.17em}= \frac{1}{3} \frac{{\mathrm{n}}_2{\mathrm{m}}_2}{\mathrm{V}} {{\mathrm{v}}_2}^2 ... \left(2\right) \end{gathered}$$

Now, from equations (1) and (2), we have

${\mathrm{m}}_1{\mathrm{n}}_1{{\mathrm{v}}_1}^2 = {\mathrm{m}}_2{\mathrm{n}}_2 {{\mathrm{v}}_2}^2 ... \left(3\right)$

Now, since temperature of both the gases is the same, the average K.E of both the gases will be same.

That is, $\frac{1}{2}{m}_1{v_1}^2 = \frac{1}{2}{m}_2{v_2}^2$       ... (4) 

So, from equation (3) and (4), we have

                      n₁ = n₂

That, is the number of molecules for both gases is the same. 

Hence, Avogadro's law is proved.