What is the formula of pressure according to kinetic theory in terms of mass density ?

In my book, the formula given is P= 1/3 nm(v^2)_(av) where n is number density, m is mass of one molecule and

(v^2)_(av) is average of square of all speeds in random direction. Now, if I were to write formula for P in terms of mass density i.e rho = m/V, it should be

P= 1/3Nrho(v^2)_(av) where N is number of molecules but the formula given in my book for this case is

P=1/3rho(v^2)_(av). What is the correct formula?

1 Answer
Jan 17, 2018

There is error in calculation of rho.
In the equation (1) m is defined as mass of one molecule. While calculating rho, m has been taken as total mass of gas sample.

Explanation:

Given

P= 1/3 nmbar(v^2) .....(1)
where n is number density, m is mass of one molecule and bar(v^2) is average of square of all speeds in random direction.

Now, writing formula for P in terms of mass density rho we see that

rho = "Total mass"/"Volume"

=>rho = nm
n being number density already stated.

Inserting in (1) we get

P= 1/3rhobar(v^2)