\(\mathrm{f}_{\mathrm{4}}\left(\mathrm{T}\right)\mathrm{=}\mathrm{A}_{\mathrm{4}}\mathrm{+}\mathrm{B}_{\mathrm{4}}\mathrm{T}\)(18)
Figure 1 Pressure-Volume diagram12
Due to the introduction of B 4, a new initial
value condition should be introduced. Hou proposed a new initial value
condition possessing a universal significance. Based on the
thermodynamic equilibrium that the Gibbs molar free enthalpy of pure
substances is equal at vapor-liquid equilibrium under a constant
temperature and pressure, the new initial value condition finally can
be
deduced as12:
\(\int_{\mathrm{V}_{\mathrm{l}}}^{\mathrm{V}_{\mathrm{v}}}\mathrm{P}\mathrm{\text{dV}}\mathrm{=}\mathrm{P}_{\mathrm{o}}\left(\mathrm{V}_{\mathrm{v}}\mathrm{-}\mathrm{V}_{\mathrm{l}}\right)\)(19)
The
establishment of the novel M-H EOS
After
rigorous
experiment calculations and a large number of data analysis about
substances in liquid-phase state and
on
the consideration of the simplicity of calculation, the novel M-H EOS is
put forward as follows:
\(\mathrm{P=}\)\(\sum_{\mathrm{i}\mathrm{=1}}^{\mathrm{5}}\frac{\mathrm{f}_{\mathrm{i}}\left(\mathrm{T}\right)}{\left[\left(\mathrm{V-b}\right)\mathrm{h}\right]^{\mathrm{i}}}\)(20)
where\({\mathrm{h=}\ \left[\frac{\mathrm{\ln}\left(\mathrm{1}\mathrm{+}\mathrm{Z}_{\mathrm{c}}\right)}{\mathrm{Z}_{\mathrm{c}}}\right]}^{\mathrm{Z}_{\mathrm{c}}}\)(21)
The
revision
factor h , which is the function of Z c, is
mainly proposed
to
correct the molar volume in liquid-phase state. The structure ofh is mainly established on the consideration
that
the derivation of the unknown characteristic constants is closely
related to the property of critical point, which can be appropriately
conveyed by a function of Z c.
After analyzing the
solving
method of unknown characteristic constants in Hou’ M-H EOS and the novel
M-H EOS, we obtain the solving method of the unknown characteristic
constants in the novel M-H EOS, which has a great improvement compared
with Hou’ method. Refer to the appendixes for the details.
DISCUSSION
ABOUT THE VERIFICATION AND APPLICATION OF THE NOVEL M-H EOS
The
analysis of the derivation about the unknown
c haracteristic
constants
The solving details of the unknown characteristic constants in the novel
M-H EOS are presented in the Appendix Ⅰ and Appendix II.
Through the analysis of the detailed derivation of the novel EOS amended
byh ,
all the initial value conditions and the simplifiedfi (T ) of the novel M-H EOS are the same
as those in Hou’s modified M-H EOS12. Meanwhile,h is a constant for a given substance, it avoids the difficulty
of the discussion about variables. However, after analyzing the
derivation process of the novel M-H EOS, we found a defect that
over-revision about some characteristic constants
maybe
exist when the state is beyond liquid-phase state because the space
between molecules will be obviously affected by temperature and
pressure
and the influence may be amplified by h because the solutions of
all the characteristic constants are affected by h in some
degree, although h is mainly designed to revise the molar volume
in liquid-phase state.
In the novel M-H EOS, only
a
minimum amount of information is necessary to characterize a
given
substance. In this work,
the
novel M-H EOS has been applied to six representative substances: argon,
methane, nitrogen, propane, benzene and water to
verify
its
generality
and calculation
precision
in liquid-phase state. The physical constants of these substances are
listed in Table 1 except\(\frac{\mathrm{R}\mathrm{=\ 82.055}\left(\mathrm{\text{atm}}\mathrm{.}\mathrm{\text{cm}}^{\mathrm{3}}\right)}{\left(\mathrm{\text{K.mol}}\right)}\)and its calculated characteristic constants are listed in Table2 37-40.
Table 1 The physical constants of given substances