Molecular flux-thermodynamic kinetics

[oxman]

1. Homework Statement

A volume is divided into two equal parts by a partition. The left volume has N atoms. The atoms have a mass m. A hole of area A is made in the partition at time t=0

A)Develop an expression for the number of white atoms on each side of the partition at time t.
B)Check your answer when t-->infinity and when t-->0
C) If the right volume is just free space how is your answer changed?



2. Homework Equations

Φ=ΔN/ΔAΔt

Phi= 1/4(v)n where n=N/V
3. The Attempt at a Solution

i got N=Noe^(vAt/4V) my teacher says this is wrong if i take t-->infinity...im pretty sure what i solved for is correct tho...

 

[mark726]

I would like to clarify a few things about the given problem and provide a solution to the best of my knowledge.

Firstly, it is important to note that the given problem does not specify the type of atoms or the conditions under which they are present. Therefore, I will assume that the atoms are non-reactive and the system is at equilibrium.

A) To develop an expression for the number of white atoms on each side of the partition at time t, we can use the formula for the flux of particles, Φ=ΔN/ΔAΔt. This can be rewritten as Φ=1/4(v)n, where n=N/V is the number of particles per unit volume.

Now, since the volume is divided into two equal parts by the partition, the number of particles on each side will also be equal. Therefore, the number of white atoms on the left side at time t is given by:

N_left = (1/4(v)n)(AΔt)

Similarly, the number of white atoms on the right side at time t is given by:

N_right = (1/4(v)n)(AΔt)

B) Checking our answer when t-->infinity, we can see that as time approaches infinity, the number of atoms on each side will also approach infinity, since there is a continuous flux of particles through the hole in the partition.

When t-->0, we can see that the number of atoms on each side will be equal to the initial number of atoms in the left volume, N. This is because at t=0, there is no flux of particles through the hole, and all the atoms are still present in the left volume.

C) If the right volume is just free space, then the number of atoms on the right side at time t will be zero, since there are no atoms present in that volume. This will not affect the number of atoms on the left side, which will still be given by N_left = (1/4(v)n)(AΔt).

In conclusion, the expression for the number of white atoms on each side of the partition at time t is N_left = N_right = (1/4(v)n)(AΔt). This is valid for all values of t, including t=0 and t=∞.