Wu Xiong(Xian modern Chemistry Research Institute,710065,China)
Theoretically speaking, the equation of state of any gases may be written in virial form.
……
(01)
where
B is the second virial
coefficient, C is the third virial coefficient,etc., V is the molar volume.
The virial equation of state
has clear physical meaning. The first term corresponds to the behavior of ideal
gases; the second term describe the action between two molecules, and the third
one considers the interaction for three molecules and so on. At lower pressure
the opportunity of interaction for more than three molecules seldom occurs, so
it is good enough to reflect the gaseous properties with former two terms, but
at high pressure the interaction of several molecules can not be neglected any
longer. In this case, the higher virial coefficients have to be considered.
Unfortunately, as the complexity increases rapidly for the higher virial
coefficients, the calculation of them become more and more difficult, except the
most simple hard spheres being used. This is why the perfect theoretical virial
equation of state has seldom been put into practies. However, It is the
statistical mechanics leads us to know that there is a relation like power
function
between higher virial coefficients and the second one.
So we try to simplify equation (01) to an expression which may be expressed by
the second one and can be used matter-of fact.
In theory, there are:
B
= b0B*(T*) (02)
(03)
(04)
(05)
(06)
the C(j) expressed by schedule method in literature.
where: B*(T*) is the second and C*(T*) is the third dimensionless virial coefficient respectively.
T* is the
dimensionless temperature. s，
are the constants of
Lennard-Jones.
From (03) and (06) we know the two series is very fast to convergence when T*>1, and may be take the first term only the other ones can be neglected, in this case:
(07)
Owing to the similarity of virial
coefficients under higher temperature, equation (07) may be extended as follows:
(n≥3)
(08)
Consequently, the nth virial coefficients can be expressed by the second one so equation (01) becomes:
(09)
(when n≥3 ，T*≥20)， (in the case of detonation, T* always >20)
where:
Expression (09)