Problem\#2 (30 points) A constant-volume stirred-tank heater can be modeled by the dynamic equation VCdtdT=wC(TiT)hA(TTa)+Q where T is the temperature in the tank and Q is the electrical heating power delivered by a resistance element. The mass flow rate w, the inlet temperature Ti, specific heat capacity C, density of the iquid and the ambient Ta are known to remain constant. The remaining modeling variables, namely the area available for heat losses A and the heat transfer coefficient h are also constant parameters. Assume that the initial condition is at steady state. 1. Obtain a transfer function that relates liquid outlet temperature T to the heating power Q. Express the transfer function in the standard format. 2. Identify the gain of the transfer function in terms of the parameters of the process. 3. Identify the time constant of the transfer function in terms of the parameters of the process