Question

The pressure exerted by an ideal gas is given
by
p = 1/3 mnv²
Using this expression deduce Avogadro's
law.

Answer 1

according to the original formula

$$p = n \frac{mv^{2}}{2}\frac{2}{3} = nkT$$

respectivly

$$N = \frac{pV}{kT}$$

and this is Avogadro's law - in equal volumes of different gases, taken at the same temperature and pressure, contains the same number of molecules.