Question

On a horizontal table there is a container standing frictionless, which is divided into two equal parts by a partition wall. In one part of the container there is oxygen, in the other part - nitrogen. The pressure of oxygen is twice as high as the pressure of nitrogen. By what distance does the container shift when the partition becomes permeable to both gases? The length of the container is l = 20 cm. Neglect the mass of the container and the partition wall.

A clear process with formulas will be highly appreciated!

Thanks

Answer 1

Let us assume that the volume of the container is V and the partition is at the middle so both the gases are occupied in the volume V/2 and with the separation wall to be at a distance l/2=20/2 =10 cm. The pressure of nitrogen gas is P so the pressure of the oxygen gas will be 2P.

here, we shall be applying the following relation

We know that the volume V=area (A) x length(l). Initially the partition is at center so V1=V2= A x l/2. Let us assume that we need to move the partition at a distance d from towards the oxygen gas from the center as shown in the figure

Using Eq. (1)

Solving for d

So the partition should shift a distance of 3.33 cm towards the oxygen side.