Process control dynamics

Consider the heated stirred tank described

in section $2\mathrm{.}4\mathrm{.}2$ and Figure $2\mathrm{.}3$ in your textbook. The model equations were developed in the class

$\frac{dV}{dt}=\frac{1}{}(w_i-w)$

$\frac{dV}{dt}=\frac{w_i}{V}(T_i-T)+\frac{Q}{V}$

For a steady state inlet and outlet flow rates of $100$ liters$/$minute$,$ a liquid volume of $500$ liters and inlet and outlet temperatures of $20$ and $40C,$ respectively.

a$.$ Find the steady state heating rate, Q$.$

b$.$ Consider a step inlet temperature change from $20$ to $25.$ Plot how the vessel temperature will change with time in the first $30$ minutes.