Chapter 5: Isothermal Reactor Design: Conversion
Deriving Total Molar Flowrate:
\(\frac{dP}{dW} = -\frac{\alpha}{2} \frac{P_0}{\left(\frac{P}{P_0}\right)} \frac{T}{T_0} \frac{F_T}{F_{T0}}\)
\(F_T = F_{T0} + F_{A0} \delta X = F_{T0} \left(1 + \frac{F_{A0} \delta X}{F_{T0}}\right)\)
\(F_T = F_{T0} (1 + y_{A0} \delta X) = F_{T0} (1 + \epsilon X)\)
\(\frac{F_T}{F_{T0}} = (1 + \epsilon X)\)
\(\frac{dP}{dW} = -\frac{\alpha}{2} \frac{P_0}{\left(\frac{P}{P_0}\right)} \frac{T}{T_0} (1 + \epsilon X)\)
\(\frac{d(P/P_0)}{dW} = -\frac{\alpha}{2} \frac{1}{(P/P_0)} \frac{T}{T_0} (1 + \epsilon X)\)