$(2\mathrm{.}7)$ For polystyrene, a relaxation time associated with con$-$

figurational rearrangements, ${}_{\text{c}\text{o}\text{n}\text{f}\text{i}\text{g}},$ follows a Vogel$-$

Fulcher law,

${}_{\text{c}\text{o}\text{n}\text{f}\text{i}\text{g}}={}_0$exp$(\frac{B}{T-T_0}),$

where ${}_0,B,$ and $T_0$ are constants, with $B=710$ and

$T_0=50C.$ A value of the experimental glass transition temperature is measured with an experiment carried out at an effective timescale $\backslash$tau $\_($exp$)=1000$s and found to be $101\mathrm{.}4\backslash$deg C$.$ a$)$ another experiment is carried out at an effective timescale of $10^5$s$.$ what is the value of the glass transition temperature that this experiment obtains? b$)$or what timescale must an experiment be carried out if it is to measure a glass transition temperature within $10\backslash$deg C$.$ of the Vogel$-$Fulcher temperature T$0?$ Is this practically possible?