The elementary reversible liquid-phase reaction takes place in a CSTR with a heat exchanger. Pure A enters the reactor.
(a) Derive an expression (or set of expressions) to calculate G(T) as a function of the heat of reaction, equilibrium constant, temperature, and so on. Show a sample calculation for G(T) at T = 400 K.
(b) What are the steady-state temperatures?
(c) Which steady states are locally stable?
(d) What is the conversion corresponding to the upper steady state?
(e) Vary the ambient temperature Ta and make a plot of the reactor temperature as a function of Ta, identifying the ignition and extinction temperatures.
(f) If the heat exchanger in the reactor suddenly fails, what would be the conversion and the reactor temperature when the new upper steady state is reached?
(g) What heat exchanger product, U_A, will give the maximum conversion?
(h) What is the adiabatic blowout flow rate, υ₀?
(i) Suppose that you want to operate at the lower steady state. What parameter values would you suggest to prevent runaway, for example, the upper SS?

Additional information:
UA=3600 cal/min⋅KE/R=20000KCPA=CPB=40 cal/mol⋅KV=10dm3ΔHRx∘=−80000⁢ cal/mol Aυ0=1dm³/min⁡KC=100 at 400kF_A0=10 mol/mink=1min−1at 400 K
Ambient temperature, T_a=37∘Feed temperature, T₀=37ºC