$5\mathrm{.}2$ In a particular adiabatic solution polymerization, the temperature $(T)$ is found to vary with time $(t)$ according to the expression:

$\frac{1}{(T-T_0)}=\frac{A}{t}+B$

For a run in which the initial monomer concentration is $0\mathrm{.}800mo\frac{l}{1}$ and the initial temperature is $50\mathrm{.}0C,A=12\mathrm{.}5mi\frac{n}{}C$ and $B=0\mathrm{.}0550C^{-1}.$ If the specific heat of the solution is $0\mathrm{.}650ca\frac{l}{}C-ml$ and the volume of the solution remains constant with conversion, calculate the following:

$($a$)$ The heat of polymerization

$($b$)$ The time for $10\%$ conversion of monomer to polymer