Problem $7\mathrm{.}1$

Using the experimental data of cloud point measurements for PS$/$PI pairs given in Table $7\mathrm{.}5,$ obtain an expression for $$ defined by Eq$.(7\mathrm{.}2)$ for each PS$/$PI pair. Use Eq$.(7\mathrm{.}4)$ for the temperature$-$dependent specific volume of PS$,v_{PS},$ and Eq$.(7\mathrm{.}5)$ for the temperature$-$dependent specific volume of PI$,v_{\frac{?}{PI}}.$ Convert $($having the units of $mo\frac{l}{c}{m}^3)$ to Flory$-$Huggins interaction parameter $$ using the definition of molar reference volume, $V_{\text{r}\text{e}\text{f}}=[(M_S{v}_{PS})(M_{\text{I}}{v}_{\frac{?}{PI}}){]}^{\frac{1}{2}}$ with $M_S$ being the molecular weight of styrene monomer and $M_{\text{I}}$ being the molecular weight of isoprene monomer. Note that $M_S=104\mathrm{.}15$ and $M_{\text{I}}=68\mathrm{.}11.$