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)
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
#rho = "Total mass"/"Volume"#
#=>rho = nm#
#n# being number density already stated.
Inserting in (1) we get
#P= 1/3rhobar(v^2)#