b) A first order reactionA→B, with the rate constant k is taking place in CSTR fed with A at concentration Car which remains unchanged. There are likely to be some deviations in the feed rate (F) of A. Derive linearized transfer function between. concentration of A in the outlet and feed rate of A assuming that volume V of reacting mixture remains unchanged.
Is the model linear? If we decide to solve the model numerically, we do not have to linearize; in fact, the non-linear model would be more accurate. However, in this problem we seek the insight obtained from the approximate, linear model.
All terms involve a constant times a variable (linear) except for the following term, which is linearized using the Taylor series..
higher order terms AAs AsAAs
This approximation can be substituted into equation 2, and the initial steady-state model subtracted to obtain the following, with C’A = CA - CAS.
This linear, first order ordinary differential equation model can be arranged into the standard form, given in the following.