Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local shape of the vapor-liquid critical point on the thermodynamic
  surface and the van der Waals equation of state   Differential geometry is powerful tool to analyze the vapor-liquid critical
point on the surface of the thermodynamic equation of state. The existence of
usual condition of the critical point $\left( \partial p/\partial V\right)
_{T}=0$ requires the isothermal process, but the universality of the critical
point is its independence of whatever process is taken, and so we can assume
$\left( \partial p/\partial T\right) _{V}=0$. The distinction between the
critical point and other points on the surface leads us to further assume that
the critical point is geometrically represented by zero Gaussian curvature. A
slight extension of the van der Waals equation of state is to letting two
parameters $a$ and $b$ in it vary with temperature, which then satisfies both
assumptions and reproduces its usual form when the temperature is approximately
the critical one.

1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int