It has been seen in Section 2 Pressure that a gas occupying partially a container evolves freely until its particles are uniformly distributed over the entire container, without changing its internal energy. We have also seen that two systems at different temperatures when held in thermal contact evolve until both reach the same temperature. In both cases the First Principle does not predict the direction in which the systems will evolve. The first Principle is compatible with the fact that the gas particles occupy all the space available in the container or just a half of it, as far as there is no work involved. It does not take care wether the system at higher temperature releases or gains energy as far as the change in the internal energy equals that energy transferred. A new concept is needed to describe all this phenomenology.
These questions are essentially related with the fact that macroscopic systems are made of a huge number of particles.
Let us consider the statement:
Consider a system
like that shown
in the simulation, but much simpler: 5 particles in a container that is
divided into 5 cells. Assume that the probability for a particle to
a given cell is the same for all cells. We could find the five
in one cell, or three in one cell and two in another one, etc. Which is
the most probable distribution?
Some of the possible distributions are shown in the figure. Click here to see the answer.
The differences in the probabilities of the different configurations are not extremely large with five particles, though they are significant. But real systems are made of a number of particles of the order of Avogadros's number, a number with 24 significant digits!
A new concept is defined, related to the number of different ways in which the particles of the system can be distributed
The new concept is related with
probability. This would seem to be something
not very deterministic in principle, but considering the large number
particles in real systems it may be understood that some deterministic
statements could be made with very high accuracy. It would not be
that all the molecules of the air in this room be concentrated in a
of the room, but nobody has died until now by that reason and we
should not worry about that!
The entropy of a system
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