A continuous stirred tank is often used to isolate a process stream to protect the downstream equipment. Thus it serves as a buffer between components such as reactors, heat exchangers,

and mixers in a processing line. A process produces species A according to a program; the concentration of A increases linearly for a period of time, levels out for a period of time, then decreases linearly for a period of time. The times and the starting and ending concentrations are always different. These differences create problems in operating the equipment downstream since each component has to adapt to the differing concentrations. An alternative is to feed species A to a continuous stirred tank just after it's produced and deliver a predictable concentration to all of the downstream equipment. In this problem, we will complete one part of the tank design by finding the response to the linear ramp up in concentration. The concentration of species A fed to a continuous stirred tank increases linearly with time at a rate E, which has units of concentration per time. We model this ramp up in the concentration as cA1 = CAm + Et, where t is time. The concentration CAm is the starting value in the feed pipe and is a constant. The volumetric flow rate in the pipe is constant although the reactant concentration varies. The continuous stirred tank has a volume V. The initial concentration of species A in the tank is CA0. Find the transient response of species A in the tank to the linear ramp up in concentration. Use the 8 step method to develop the model. For the purpose of this problem, let CAm = CA0. How is time zero defined?