Intermolecular forces and Transport phenomena

[jacobtwilliams001]

Homework Statement

There is a small uniform pressure gradient in an ideal gas at constant
temperature, so that there is a mass flow in the direction of the gradient. Using the mean
free path approach show that the rate flow of mass in the direction of the pressure
gradient per unit of area and per unit pressure gradient is mv(average)l/3kT.

Relevant Equations

mean free path: l=1/n*sigma
mass of flow rate: m^degree=rho*V*A
Kinetic Theory:
PV=NkT
NkT=1/3*Nm*v(average)^2
1/2*m*v(average)^2=3/2*kT

I am able to find and understand T from kinetic theory, but I do not understand how to use pressure gradient per unit of area and per unit pressure gradient.

 

[mjc123]

There is no such thing as "pressure gradient per unit of area". What the question wants, though the wording is perhaps a bit unclear, is the rate of mass flow per unit area and per unit pressure gradient, the mass flow being in the direction of the pressure gradient.
I.e. (1/(A*dP/dx))*dm/dt