McMaster UniversitySolutions for Tutorial 4The Transfer Function and Combined Models4.1 Isothermal CSTR with two input changes: This question builds on the resultsfrom tutorial Questions 3.1 and 3.2. Consider a CSTR with the following reactionoccurring in the reactor0.5A → B- r = kCA AAssuming 1) the reactor is isothermal, 2) the reactor is well mixed, 3) density of thereactor content is constant, and 4) the reactor volume is constant.a. Derive the linearized model in deviation variables relating a change in C on theA0 reactor concentration, C .Ab. Derive the linearized model in deviation variables relating a change in F on the reactor conc .Ac. Determine the transfer functions for the two models derived in parts a and b.d. Draw a block diagram relating C and F to C .A0 Ae. The following input changes are applied to the CSTR:1. A step change in feed concentration, C , with step size ∆C at t , andA0 A0 C2.geflow rate, F, with step size ∆F at t .> t .F CWithout solving the equations, sketch the behavior of C (t).Aa/c. The model for the change in C (with the subscript meaning the input changeA0C ). The model for this response has been derived in previous tutorial question 3.1, andA0the results are repeated in the following.dC' V FAτ + C' = K C' with K =τ =CA0 A CA0 A0 CA0 CA0−0.5 −0.5dt F + 0.5VkCF + 0.5VkC As AsK (C (s)) KCA0 A CA0 CA0(1) (C' (s)) = C' (s) transfer function =A CA0 A0τ s +1 C (s) τ s +1CA0 A0 CA0−t / τCA0C' (t) = ∆C K()1− eA A0 ...