Problem $4$:

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We discussed the Young$-$Laplace equation: $P_{\text{c}\text{u}\text{r}\text{v}\text{e}\text{d}}=P_{\text{f}\text{l}\text{a}\text{t}}+(\frac{1}{r_1}+\frac{1}{r_2}{)}^{*}$ to describe the vapor pressure at

a curved surface. Increased curvature will correspond to a decreased radius. In the equation, $$ is the

surface energy. Use graphing software to make a plot showing the change in equilibrium vapor

pressure with radius of curvature for two spherical particles from $1$ nm to $1$ mm at $770C$ which has a

$P_{\text{f}\text{l}\text{a}\text{t}}$ value of $3\mathrm{.}4{10}^{-4}$ Torr. The molar volume of the material is $1\mathrm{.}6{10}^{-5}{m}^3$ and the surface energy is

$0\mathrm{.}56J{m}^{-2}.$ To do this problem correctly, the units on the given quantities will have to be consistent.