Solution:
Please explain the phenomenon of “multiple steady state” in a nonisothermal CSTR running an exothermic and first–order reaction and define the condition of runaway point mathematically.\\
Hint : By neglecting the shaft work and assuming $\Delta C_p = 0$,\\
$- X \Delta H_{Rx}^{\circ} = C_{p0} (1 + \kappa) (T – T_c)$\\
where $C_{p0} = \sum \Theta_i C_{pi}$ ; $\kappa = (UA / C_{p0} F_{A0})$ ; $T_c = (\kappa T_a + T_0) / (1 + \kappa)$\\
($X$ : conversion ; $\Delta H_{Rx}^{\circ}$ : heat of reaction ; $U$ : overall heat transfer coefficient ; $A$ : heat transfer area ; $T_a$ : coolant temperature)
