The Semenov theory of ignition is based on the hypothesis that a critical temper

Question

The Semenov theory of ignition is based on the hypothesis that a critical temperature exists where the heat produced by chemical reaction is equal to the heat removed by cooling through the walls of the vessel. The point where the derivatives of the heat produced and lost with respect to temperature are equal represents a unique interesting temperature which is called as ignition temperature. Derive the following Semenov Equation, and answer the following questions. ln[P/T_c^(n+2)/n] = ln{(hsR^n+1)/(delta HVAX_A^nE)} E/nRT_c where P pressure, T_c = the ignition temperature, h = heat transfer coefficient, S = surface area of combustion chamber, R = gas constant, delta H = enthalpy of formation, V = volume of combustion gas or combustion chamber, X_A = fuel mole fraction, E = activation energy. (1) Using Semenov Equation, explain the ignition temperature increases or decreases when the fuel mixture becomes lean, and (2)

Explanation / Answer

When the fuel mixture becomes lean then the ignition temperature decreses...When we talk about "temperature" of something, we are really talking about how fast the molecules are moving around and bouncing off each other. "Temperature" is really "kinetic energy". And it turns out that there are other types of energy besides moving around in space -- molecules can rotate, they can vibrate, and their electrons can get excited and move around relative to the nucleus. Each of these energies can also be a "temperature", so you can have translational temperature (what we normally think of), but you can have rotational temperature, vibrational temperature, and electronic temperatures.By changing the amount of fuel in the mixture, you are changing the types of collisions that can occur. And it's not exactly straight forward, but some molecules are better at exchanging energy with others. To make the fuel molecule fall apart, they need to collide with other fuel molecules with some energy of with other oxygen molecules with more energy. If you add more than the usual amount of oxygen (run lean), you also need to make that oxygen hotter so the molecules have more energy when they collide and can make the fuel vibrate hard enough to fall apart. Conversely, if you run fuel-rich, you have more fuel molecules that can collide with one another and fall apart, but fewer oxygen molecules for them to combine with and give off heat. This (and some other effects) makes the final flame temperature lower.

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