The following irreversible elementary liquid phase reaction is taking place in a $0\mathrm{.}01$ m$3$ PFR which is mounted with a heat exchanger.

$2$ C$4$H$4---->$ C$6$H$5$CH$=$CH$2$

The feed at $400$ contains only C$4$H$4$ and the concentration of C$4$H$4$ in the feed is $1$ kmol$/$m$3$ and the molar flow rate of it is $300$ mol$/$min$.$ The heat capacities of C$4$H$4$ and C$6$H$5$CH$=$CH$2$ are $122$ J$/$mole$.$K and $244$ J$/$mole$.$K$,$ respectively. The $$Ua$$ value for the heat exchanger is $5000$ J$/$s$.$dm$3/$K and the heat exchanger fluid has a temperature of $425.$ The heat of reaction $($Hrxn$)$ and the rate constant $($k$)$ of the reaction are a function of temperature according to the following expressions:

$$Hrxn $=-23100012($T$-25)$ J$/$mole where T is in $$

k $=1\mathrm{.}48$ x $108$ exp $(-19124/$T$)$ dm$3/$mole$.$s where T is in K

Determine the conversion of C$4$H$4$ that can be achieved in this reactor. please use mathlab or polymath and find conversion of A$.$