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?
In my book, the formula given is
1 Answer
There is error in calculation of
In the equation (1)
Explanation:
Given
P= 1/3 nmbar(v^2) .....(1)
wheren is number density,m is mass of one molecule andbar(v^2) is average of square of all speeds in random direction.
Now, writing formula for
rho = "Total mass"/"Volume"
=>rho = nm
n being number density already stated.
Inserting in (1) we get
P= 1/3rhobar(v^2)