Question 8.3.4: Heat Capacity of a Mixture Calculate the heat required to br......
Heat Capacity of a Mixture
Calculate the heat required to bring 150 mol/h of a stream containing 60% C_{2}H_{6} and 40% C_{3}H_{8} by volume from 0°C to 400°C. Determine a heat capacity for the mixture as part of the problem solution.
Neglecting changes in potential and kinetic energy and recognizing that there is no shaft work involved in the process, the energy balance becomes \dot{Q} = \Delta \dot{H} = \dot{n} \Delta \hat{H} where \Delta \hat{H} = \int_{0°C}^{400°C}{(C_{p})_{mix} dT} . The polynomial expressions for the heat capacity of ethane and propane given in Table B.2 are substituted into Equation 8.3-13 to yield
(C_{p})_{mix} (T) = \sum\limits_{\begin{matrix} all\\ mixture\\ components\end{matrix} }{y_{i}C_{pi}(T)} (8.3-13)
If potential and kinetic energy changes and shaft work are neglected, it follows that
\dot{Q} = \Delta \dot{H} = \dot{n} \Delta \hat{H} =\begin{array}{c|c}150 mol &34.89 kJ \\ \hline h&mol\end{array} = \boxed{5230 \frac{kJ}{h}}
As usual, we have assumed that the gases are sufficiently close to ideal for the formulas for C_{p} at 1 atm to be valid.