Problem 2: Modeling a Non-Isothermal Plug Flow Reactor (PFR) Consider an exothermic, first-order reaction in a plug flow reactor. The reaction rate constant k(T) = k0 * exp(-Ea/(RT)), where k0 = 1e6 1/s, Ea = 50000 J/mol, R = 8.314 J/(molK), and the initial temperature is 300 K. Model the temperature profile along the length of the reactor, assuming a heat transfer coefficient U = 100 W/(m^2*K) and an ambient temperature Ta = 300 K.