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Problem

The simplest description of liquid-gas interface: a sharp transition

$\begin{displaymath} \rho = \begin{cases} \rho_l, & x<0\\ \rho_g, & x\gt \end{cases}\end{displaymath}$

$\begin{figure} \psfrag{z}{$x$} \psfrag{rho}{$\rho$} \includegraphics{sharp}\end{figure}$
A more refined version--smooth transition:
$\begin{figure} \psfrag{z}{$x$} \psfrag{rho}{$\rho$} \includegraphics{smooth} \end{figure}$

Problems:

1.: Calculate the profile $\rho(x)$ and the width of the interface
2.: Calculate the surface tension $\gamma$
3.: What happens as $T\to T_c$ ?