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\sect{Chemical equilibrium A[volume]-A[surface]}


Consider a tank with water volume ${V}$,and over it oil is
floating.The surface contact between the water and the oil is ${S}$.
In the water and over the contact surface between the water and the
oil, large molecules with mass ${\mathsf{m}}$ are moving. Assume
that the potential energy of each molecule is ${E_{1}}$ when it's in
the water, and ${E_{2}}$ when it's on the boundary between the water
and the oil ${\left(E_{2}>0,E_{1}>0\right)}$
${E_{2}-E_{1}=E_{0}>0}$.

Assume that the large molecules are classical ideal gas
(which means there's no interaction between the large
molecules).What is is the system's temperature ${T}$ ?

\begin {itemize}

\item[a]
Calculate the chemical potential ${\mu_{l}}$ of the large molecules
in the water.

\item[b]
Calculate the chemical potential ${\mu_{s}}$ of the large molecules
on the boundary between the water and the oil.

\item[c]
What is the ratio between the large molecules density in the water,
and their density on the boundary between the water and the oil in
equilibrium?

\item[d]
What is the total energy of the large molecules?

\end {itemize}