Consider the stirred$-$tank heater shown in the Figure below. The process model for this system is

$C_{p}V\frac{dT}{dt}=C_{p}F(T_{in}-T)+Q$

Where the liquid density has a specific gravity of $0\mathrm{.}9\frac{g}{m}L,$ the heat capacity $(C_p)$ is equal to $0\mathrm{.}8ca\frac{l}{g}-C,F$ is $100k\frac{g}{m}in,T_{in}$ is $20C,V$ is $200$ Liter and initially $T$ is $75C.$

Determine the transfer function, the time constant and the process gain.