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reaction_rate_equation [2013/10/14 09:50] nikolaj |
reaction_rate_equation [2015/08/15 20:33] nikolaj |
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| ===== Reaction rate equation ===== | ===== Reaction rate equation ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $R,J\in \mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $R,J\in \mathbb N$ | |
| - | | @#88DDEE: $ \nu^-,\nu^+\in\mathrm{Matrix}(R,J,\mathbb Q) $ | | + | | @#55CCEE: context | @#55CCEE: $ \nu^-,\nu^+\in\mathrm{Matrix}(R,J,\mathbb Q) $ | |
| - | | @#88DDEE: $ k\in \mathbb R^R $ | | + | | @#55CCEE: context | @#55CCEE: $ k\in \mathbb R^R $ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $ [A] \in \mathrm{it} $ | | |
| - | | @#FFBB00: $ [A] \in \mathrm{it} $ | | + | |
| | $j\in \text{range}(J)$ | | | $j\in \text{range}(J)$ | | ||
| - | + | | @#55EE55: postulate | @#55EE55: $ [A]:C(\mathbb R,\mathbb R^J) $ | | |
| - | | @#55EE55: $ [A]:C(\mathbb R,\mathbb R^J) $ | | + | | @#DDDDDD: range | @#DDDDDD: $ ::[A](t) $ | |
| - | + | | @#55EE55: postulate | @#55EE55: $ \frac{\partial}{\partial t}[A]_j=\sum_{r=1}^R k_r\cdot(\nu_{rj}^+-\nu_{rj}^-)\cdot\prod_{i=1}^J [A]_i^{\nu_{ri}^-} $ | | |
| - | | @#DDDDDD: $ ::[A](t) $ | | + | |
| - | + | ||
| - | | @#55EE55: $ \frac{\partial}{\partial t}[A]_j=\sum_{r=1}^R k_r\cdot(\nu_{rj}^+-\nu_{rj}^-)\cdot\prod_{i=1}^J [A]_i^{\nu_{ri}^-} $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| e.g. the simplest carbon combustion process | e.g. the simplest carbon combustion process | ||
| - | $CH_4 + 2\ O_2 \longrightarrow CO_2 + 2\ H_2O $ | + | $\mathrm{C}\mathrm{H}_4 + 2\ \mathrm{O}_2 \longrightarrow \mathrm{C}\mathrm{O}_2 + 2\ \mathrm{H}_2\mathrm{O}.$ |
| - | + | ||
| - | or more explicitly | + | |
| - | $1\ CH_4 + 2\ O_2 + 0\ CO_2 + 0\ H_2O \longrightarrow 0\ CH_4 + 0\ O_2 + 1\ CO_2 + 2\ H_2O $ | + | (Or more explicitly |
| + | $1\ \mathrm{C}\mathrm{H}_4 + 2\ \mathrm{O}_2 + 0\ \mathrm{C}\mathrm{O}_2 + 0\ \mathrm{H}_2\mathrm{O} \longrightarrow 0\ \mathrm{C}\mathrm{H}_4 + 0\ \mathrm{O}_2 + 1\ \mathrm{C}\mathrm{O}_2 + 2\ \mathrm{H}_2\mathrm{O}$.) | ||
| In practice, $k$ depends on the temperature, which, through the equation of state, can again be a nonlinear function of the concentrations. | In practice, $k$ depends on the temperature, which, through the equation of state, can again be a nonlinear function of the concentrations. | ||
