26. Systems with a large number of particles and the laws of mechanics

The properties of any body are determined by the properties and movement of the particles composing it. Let's consider, for example, how the pressure of gas arises on the walls of a vessel.

Let the gas be in a closed vessel. The pressure meter shows a certain gas pressure \( p_0 \). But how does this pressure appear? If a molecule hits a wall, it will affect the wall with a certain amount of force for a short period of time. As a result of random impacts on the wall, the force acting from the molecules per unit of the wall area, i.e. the pressure, will change very quickly over time, approximately as shown in the graph. However, the actions caused by the impact of individual molecules, the meter is not recorded, because the molecules are very small. Therefore, the meter registers the average pressure \( p_0 \) acting on its membrane. It is also shown on the graph in blue line. Despite small changes in pressure, this average value \( p_0 \) is practically defined value because of the fact that there are a lot of impacts on the wall.

It is easy to explain why the gas is exerting pressure on the walls of the vessel. But calculating the average pressure is not that easy. After all, the pressure depends on the movement of all gas molecules, and the number of them is huge, and to determine the trajectories of all molecules is not possible.

However, the task of researching systems of large numbers of particles on the basis of certain notions of the structure of the substance can be solved. The behavior of such systems as a whole reveals not so complex regularities. But these are laws of a new type, the laws of molecular-kinetic theory, or statistical mechanics.

For describing the properties of macroscopic bodies and processes that we observe on experiment, it is not necessary to know the character of motion of individual particles. It is important to know not the behavior of individual molecules, but the average result to which their aggregate motion leads. This result can be predicted with the help of molecular-kinetic theory.