Consider the $f$ constant volume heating tank as in Question$1.$ The tank is operating at design conditions. The tank temperature is now measured with linear electronic transmitter $($span $10$ to $90C).$ The electronic heater is linear with maximum heat output of $160kW.$ A proportional controller is attached with a proportional PB $=50.$

Design Conditions:

Inlet temperature; $T_i=10C$

Outlet temperature; $T=50C$

Tank Volume; $V=0\mathrm{.}1m^3$

Heat capacity; $C_p=4\mathrm{.}0\frac{J}{g}*C$

Heater; electronic; $Q=80kW$

a$)$ Determine the steady state signal, $T_m,T_{sp},E,$ and $p$

b$)$ Determine the closed$-$loop transfer function, $G_{m(s)},G_{c(s)},G_{v(s)}$

c$)$ Is the closed loop system stable? Explain why?

And find the offset