The control system of the steam-jacketed kettle is shown in the figure. The system consists of a kettle throughwhich water flows at a variable rate w (k9/s). The entering water is at temperature T; ("C), which may varywith time. The kettle water, which is well agitated, is heated by steam condensing in the jacket at temperature T,and pressure P, . The temperature of the water in the kettle is measured and transmitted to the controller. Theoutput signal from the controller is used to change the stem position of the valve, which adjusts the flow of steamto the jacket w.|Computer/ControllerThe following assumptions are made for the kettle:• The hold-up volume of water in the kettle is constant.The thermal capacity of the kettle wall, which separatessteam from water, is negligible compared with that of theTemperature-measuringelementWaterwater in the kettle.The heat capacities of water cpw (K/kg°C) and themetal wall Cp,methal (K/kg°c) are constant.The density of water is constant Pw (k9/m3)• The temperature of the steam in the jacket T, = T, (°C) isControl valveSteamJacketwallWeT. Condensateconstant.Figure 1.a) Develop a set of differential equations required to simulate the temperature change of the water To as afunction of w, T; and Ty.b) Develop the transfer function between water T, and w, T; and Tyc) Represent the transfer function in a block diagram

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