To Prove P= NKT

Show that
P = Nv KT
Where Nv = No of molecules per unit volume
Proof
According to kinetic equation of pressure
P = 1/3 r v2 ………………(1)
We know that:
r = mass / volume
r = mN / V
Putting the value of “r” in equation (1)
P = 1/3 mN/V v2
P = 1/3 N/V mv2……………(2)But N/V = no of molecules per unit volume
i.e.
N/V = Nv
Putting the value of N/V in eq (2)
P = 1/3 Nv mv2
Multiply and dividing by 2 on R.H.S
P = 2/3 Nv (1/2mv2)
P = 2/3 Nv 3/2 KT [1/2mv2 = 3/2 KT]
P = Nv KT