A steam coil is used to heat a process liquid from A₁ ^oC to A₂ ^oC which is continuously fed into the perfectly mixed tank as shown in FIGURE Q1. The feed rate w₀ is 0.48 m³/min material with a constant density of 800 kg/m³ and heat capacity of 2.1kJ/kg-K. The holdup in the tank is constant at 2.25 m³. The latent heat of vaporization _s is 2093.4 kJ/kg. Steam is added at a rate w_s kg/min.

FIGURE Q1. Stirred tank heater

1. Determine the transfer functions of the process.
2. Determine the gains and time constants of the process.
3. If the disturbance variable suddenly increases to A₃ ^oC what will be the new value of the outlet temperature after the process reaches a new steady state value.
4. How long does the process take to reach, 99%, of the new steady state value?
5. The operator wants to return the process to the initial steady state by introducing a step change in the steam flow rate. Determine the step size required to return the outlet temperature to the initial steady state value?
6. How long will the process take to reach the 99.3% of the steady state value after the change in part (e) is introduced?
7. Determine the response of the process for a step change of size 2 in the manipulated variable (disturbance does not change) and sketch the response.
8. Determine the response of the process for a step change of size 2 in the in disturbance ( MV does not change) and sketch the response.

Sure to upvote if all questions are answered in detailed! Truly appreciate your effort. Thank you in advance.

90, TO 9, T 0000 WS