A stream of wet sugar solution is fed to an evaporator in which some of water in the wet sugar is vaporized through temperature manipulation. The unit of the stream is identified as a mass flow rate and the mass fraction unit is used to measure the wet sugar composition. Assume all mass flow rates are constant and the initial inlet and outlet temperatures are set at room temperature. The density and heat capacity of sugar are assumed 1.8 kg/m3 and 0.4255 kJ/kg.K, respectively. The volume of mixture is 6 m3. Derive energy balance in the form of deviation for the given system. State your assumptions. Then, develop first order transfer functions that relates output and input variables. Calculate the values for process gains and time constants based on developed transfer functions.