Deduce Avogadro's law based on kinetic theory.

Explanation

Avogadro's law states that , at constant temperature and pressure, equal volumes of all gases contain the same number of molecules . For two different gases at the same temperature and pressure , according to kinetic theory of gases,
From equation,
`P=1/3N/Vmbar(v^(2))`
We get,
`P=1/3N_1/Vm_1bar(v_1^2)=1/3N_2/Vm_2bar(v_2^2)" "....(1)`
where `bar(v_1^2) and bar(v_2^2)` are the mean square speed for two gases and `N_1 and N_2` are the number of gas molecules in two different gases.
At the , same temperature , average kinetic energy per molecule is the same for two gases.
`1/2m_1bar(v_1^2)=1/2m_2bar(v^2)" "...(2)`
Dividing the equation (1) by (2) we get, `N_1 = N_2` .
This is Avogadro's law. It is sometimes referred to as Avogadro's hypothesis or Avogadro's Principle.