Question

When speaking of particle in a box why do the “softer” walls of real-life lead to longer box lengths than those obtained from a PIB-like rigid model used when calculating the lengths mathematically?

Answer 1

As we are speaking about gas particles in a box, we know particles are always in motion and keep vibrating. We consider square box in which gas particles are trapped so the particles are restricted to square plane. So the each particle in a straight line and in the same direction and speed with which it starts until and unless it hits the wall of box.

When the molecule hits the wall of box then it changes its direction but speed remains same. As in maths, each row of matrix stores the necessary information on different particle. As in this we consider particle is in square plane so it has four sides two of them give its possition in plane and other two describe the speed of the particle in two direction x and y. Thus, the matrix in this case has four columns and rows for different particles. After every time step of particles, the (x,y) possition of the particle gets updated depending upon its velocity.

In the rigid model, the particles are in motion but in definate space and they do not collide with each other so there are less possiblities for the particles to change their direction.