Relax the restriction that there is no A inside of the isothermal CSTR at time zero. Instead the concentration of the reactant A is cA, which is not zero, when the reactor is started. The other conditions hold, namely the reaction is irreversible and first-order with rate coefficient k, and both the volumetric flow rate Q and concentration of A in the feed cA; are constant. Develop an equation to model the concentration of reactant A as a function of time, which is called the transient response. Use the 8 step method to develop the model and solve the differential equation using the integrating factor method. Examine the limiting cases based on time, t → 0 and t → 0, and briefly describe the significance of the results.

Fig: 1