please solve in 50 minutes , i will give you two likes

Q2. (a) A vat of liquid is heated by a saturated steam coil as shown in Figure Q2a. The system equations are given by d pov To = UAcou(Ts - To dt where p is the density of the liquid, Cp is the liquid heat capacity, V is the volume of the liquid, T, is the temperature of the liquid, U is the overall heat transfer coefficient between the steam and the liquid respectively, Acoil is the heat transfer area of the heating coil and Ts is the temperature of the steam in the coil. Mixer 0000 T Figure Q2a Liquid heating system i) What are the inputs and outputs of the system? 1 mark ii) What is the time constant of the system? 2 marks iii) Sketch the time domain response of the system to a unit step input. 2 marks What are some simplifying assumptions that have been made regarding the system? 2 marks iv)