Chapter 11: Nonisothermal Reactor Design: The Steady State Energy Balance and Adiabatic PFR Applications

Learning Resources

Second Order Reaction Carried Out Adiabatically in a CSTR

5. Determine T:

From the adiabatic energy balance (as applied to CSTRs):

\( T = \frac{X \left[ -\Delta H_{Rx}(T_R) \right] + \sum_i \theta_i C_{Pi} T_0 + X \Delta C_P T_R}{\sum_i \theta_i C_{Pi} + X \Delta C_P} \)

For this problem:

\( \Delta C_P = C_{PB} - C_{PA} = (15 - 15) \, \text{cal/mol} \cdot degree C = 0 \)

which leaves us with:

\( T = \frac{X \left[ -\Delta H_{Rx}(T_R) \right] + \sum_i \theta_i C_{Pi} T_0}{\sum_i \theta_i C_{Pi}} \)

After some rearranging we are left with:

\( T = T_0 + \frac{X \left[ -\Delta H_{Rx}(T_R) \right]}{\sum_i \theta_i C_{Pi}} \)