The van der waals excluded volume b = 0, 0.2 and 0.4 corresponds to benzyne gases
Answers
DOI: 10.1007/s10910-007-9272-4
Journal of Mathematical Chemistry, Vol. 43, No. 4, May 2008 (© 2007)
The van der Waals equation: analytical and approximate
solutions
Mario N. Berberan-Santos
Centro de Qu
́
ımica-Fısica Molecular, Instituto Superior Tecnico, Lisboa P-1049-001, Portugal
E-mail: [email protected]
Evgeny N. Bodunov
Department of Physics, Petersburg State Transport University, St. Petersburg 190031, Russia
E-mail: [email protected]
Lionello Pogliani
∗
Dipartimento di Chimica, Universit
`
a della Calabria, via P. Bucci, 14/C, Rende CS I-87036, Italy
E-mail: [email protected]
Received 8 February 2007; Revised 23 February 2007
The thermodynamic properties, enthalpy of vaporization, entropy, Helmholtz func-
tion, Gibbs function, but especially the heat capacity at constant volume of a
van der Waals gas (and liquid) at the phase transition are examined in two different
limit approximations. The first limit approximation is at the near-critical temperatures,
i.e., for
T/T
c
→
1, where
T
c
is the critical temperature, the other limit approximation
is at the near-zero temperatures,
T
→
0. In these limits, the analytical equations for
liquid and gas concentrations at saturated conditions were obtained. Although the heat
capacities at constant volume of a van der Waals gas and liquid do not depend on the
volume, they have different values and their change during the phase transition was cal-
culated. It should be noticed that for real substances the equations obtained at the near-
zero temperature are only valid for
T>T
triple point
and
T
T
c
, which means that
found equations can be used only for substances with
T
triple point
T
c
.
KEY WORDS:
thermodynamics, van der Waals equation, phase transition,
heat capacities, critical temperature