Consider specific volume change as a function of temperature of

polypropylene shown next.

$($a$)$ Derive the following thermodynamic relation.

$(\frac{\text{d}\text{e}\text{l}\text{G}}{\text{d}\text{e}\text{l}\text{P}}{)}_T=V$

$($b$)$ If pressure is increased, expect possible variation$($s$)$ in $V_f^{**}.$ State the

reason$($s$)$ for your answer.

$($c$)$ If the methyl side group of the polypropylene is changed to phenyl

group, expect possible variation$($s$)$ in both $V_f^{**}$ and $T_g*$ State the

reason$($s$)$ for your answer.

Hint: Use the following relation, $G=H-TS.$