The two questions below are related to the $T_g$ of poly$($methyl methacrylate$)($PMMA$).$

a$.$ Determine the $T_g$ for two PMMA samples that both have $M_n=10,000\frac{g}{m}ol.$ One sample is

linear, whereas the other has an average of seven chain ends. $K$ and $T_g^{}$ values are $6\mathrm{.}9{10}^4$

$C\frac{g}{m}ol$ and $110C,$ respectively.

b$.$ Determine the relative viscosity change for two PMMA samples from Question $1$a at $T=$

$150C.$ Assume that $C_{1,g}=34$ and $C_{2,g}=80C$ are constant for two PMMA samples when

the reference temperature is set to the $T_g$ of the samples under consideration.