Consider an electrically heated stirred$-$tank process $($shown below$)$ in which the process design and operating conditions are characterized by the following four parameter groups:

$\frac{m}{w}=25$min,$\frac{m_e{C}_e}{h_e{A}_e}=2\mathrm{.}5$min,$\frac{m_e{C}_e}{wC}=3\mathrm{.}57$min,$\frac{1}{wC}=0\mathrm{.}002$Cmi$\frac{n}{k}$cal

The process is initially at the steady state with nominal values of $Q=2000$kca$\frac{l}{m}in$ and $T_i=70C.$

a$)$ Use a computer software to calculate the response, $T(t),$ to a sudden change in $Q$ from $2000$ to $2800$kca$\frac{l}{m}in.$

b$)$ Repeat part $($a$)$ while neglecting the dynamic of the heating element temperature.

c$)$ Plot the results for parts $($a$)$ and $($b$)$ on one chart. Comment on the resulting curves.