We've stressed that our analysis of systems rests upon knowing just a
few variables, instead of trying to find out variables affecting
individual particles. To this end, we will talk about 6 variables in
particular that can be used to determine the energy of a system.
We have already been introduced to the
entropy σ and the
temperature τ as variables. There are
two more variables that are so common in everyday usage that they don't
warrant a close look, namely the number N of particles in a system and
the volume V of a system. That leaves two more variables to
understand before we can dive into the study of systems.
The Chemical Potential
Suppose that we have two systems, each consisting of the same single
chemical species, which come into thermal and diffusive contact (meaning
that particles can move between them). Note that thermal contact alone
prohibits such an exchange. Imagine what happens when you touch a
radiator - there is certainly a thermal contact, as you feel the heat of
the radiator. However, there isn't much of a diffusive contact, as your
hand doesn't suddenly melt into the radiator and become replaced in part
by metal!
Now, our chemical intuition tells us that the particles will flow from
the denser system to that which is less dense. We will formalize this
notion by introducing the chemical potential μ, which governs
how particles will flow between two systems. For now, we can think of
the chemical potential as follows:
The chemical potential can be defined in different manners as well, and
we will address this shortly.
Nevertheless, we can say now that particles will flow from a system with
a higher chemical potential to a system with a lower chemical potential
if the two are in diffusive and thermal contact.
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