So now we need to try to figure out an answer to our second question: Why does the plunger move so that the air particle density around the syringe and inside the syringe are the same?
One thing that you should notice is that there are air particles (inside the syringe) pushing up on the bottom of the plunger and air particles (around the syringe) pushing down on the top of the plunger at the same time. So how does the plunger “know” which way to go? Well, it doesn’t. Remember, syringes don’t have brains!
But let’s try a little thought experiment. Visualize two boxes connected with a movable wall. The particles in the box to the left will push the movable wall to the right. And the particles in the box to the right will push the movable wall to the left. So where will the movable wall end up?
If you adjust the particle densities in the two boxes, you will see that the wall will move until the particle densities on both sides are nearly equal. If the wall moves to the right, the particle density in the left box will decrease as its volume increases and the particle density in the right box will increase as its volume decreases. If the wall moves to the left, the opposite will happen. So why does the wall stop moving when the particle densities on both sides are nearly equal? Well, you should also notice that when the particle density on both sides are nearly equal, the collision rate on both sides are also nearly equal. This means that the wall is being pushed equally from both sides. When that happens, the forces balance out and the wall stops moving.