Write a dynamic model for the reactor only (not including the pump and heat exchanger) that\ predicts the composition (cA3, cB3, and cC3) and temperature (T3) of the reactor effluent. Use\ an appropriate number of material and energy balance equations. This is only slightly more\ complicated than the CSTR model introduced in section 2.4.6 on page 26 of Seborg Assume:\ i. The concentrations, cij , are molar concentrations and the flow rates, qj , are volume flow\ rates.\ ii. The chemical reaction is A + 2B -> C, with a rate that is given by r = kcAc2\ B . The rate\ coefficient is a constant parameter, independent of temparture.\ iii. The density (\\\ ho ) and heat capacity (C) of the process streams are constant.\ iv. Heat is transferred to the reactor contents from the heating coil at a rate:\ Qcoil = U A(TS T3)\ where U and A are both known constant parameters. The reaction is endothermic, with a\ heat of reaction HR. There is no other heat loss or gain (e.g., to or from the surround-\ ings). The conversion of shaft work and friction work to thermal energy is negligible.\ v. The reactor is well-mixed, and operates at constant volume, V .\ vi. Stream 1 contains no B or C, and stream 2 contains no A or C. (Both streams may\ contain other non-reacting species.)\ vii. The feed stream compositions and temperatures may vary with time. q1 is constant. q2\ may vary with time.\ (b) Simplify your model by eliminating q3, Qcoil, and r, by substituting the rate eqautions and\ (steady-state) total mass balance into your (dynamic) component and thermal energy balances.\ 1\ (c) The following quantities are known: HR, \\\ ho , C, k, U A, q1, and V . Perform a degree of\ freedom analysis on the model, including assigning DVs and MVs. (Note that the valve on the\ steam supply manipulates the steam pressure in the coil, thereby determining the saturation\ temperature, TS .)\ (d) Show that when T1 = T2 = Tin and HR = 0 the thermal energy balance simplifies to:\ dT3\ dt = 1\ \\\\tau r\ (Tin T3) 1\ \\\\tau ht\ (TS T3)\ where \\\\tau r is the residence time of the reactor and \\\\tau ht is a characteristic time constant for heat\ transfer. Show also that when the steam heat is completely turned off, the energy balance is\ further simplified to: dT3\ dt = 1\ \\\\tau r\ (Tin T3)