The following data for the glass transition temperature $T_g$ of polystyrene is available:

$($a$)$ What would be the glass transition temperature of a theoretically infinite molecular weight sample?

$($b$)$ Given a sample of polystyrene made by blending eight separate fractions, each of which has a very

narrow molecular mass distribution, use an appropriate average molecular weight of the sample to

determine its glass transition temperature with the Flory$-$Fox equation.