Question

Prove that pressure pressure of ideal gas p=2/3E

Answer 1

We have PV =1/3 [mNc2] but c2 is proportional to the absolute temperature T.

For a given mass of gas at constant temperature 1/3 [mNc2] is constant and therefore PV is constant and this is Boyle's law. 

The Ideal Gas equation for n moles of gas is PV = nRT and so for one mole of gas we have PV = RT, where R is the gas constant. But in one mole of gas there are NA molecules where NA is the Avogadro constant (6.02x1023) and therefore:

PV = (1/3)[mNAc2] = RT
Therefore: 1/3 [mc2] = RT/NA = kT

and the quantity k (= R/NA) is known as Boltzmann's constant (k) .

The equation for one molecule may therefore be rewritten as: 

(1/3)[mc2] = kT
this is the answer