Autoignition Temperature Derivation

[lyadalachanc]

According to Wikipedia, the autoignition is defined as:

What is the derivation of this equation? Is there even a derivation?

[studiot]

Do you mean this equation?

What do you not understand about it?

Edited February 12, 2019 by studiot

[Endy0816]

Recommend thinking about it in terms of activation energy for the chemical reaction taking place.

[lyadalachanc]

Studiot, I understand the equation, just not the derivation of it. How was the equation derived

[studiot]

Activation energy is not required.

It is just a standard bit of engineering.

If you place a sample of combustible material at temperature T₀ < less than its auto ignition temperature into an airstream which is at T_ig (or above though the equation does not allow for this possibility) then heat will be transferred from the air to the body.

If the air temperature is < T_ig then the sample will never be raised to a sufficient temperature to ignite.
So we can measure T_ig by having an air source that we can steadily raise the temperature of until ignition occurs.

This heat transfer will depend upon the surface area of the sample since it is only necessary to ignite the surface layer, not to heat up the entire sample to T_ig

For combustion to then be self sustaining it is necessary for the heat of combustion to be sufficient to raise interior parts of the sample to T_ig

This will be where the 4pi factor comes in - it is the surface area to voume ratio of a sphere.

Obviously the density and heat capacity are specified in terms of mass.

 

Does this help?

[lyadalachanc]

I don't understand how the interior of a material is related to the ratio of the surface area to the volume of a sphere. Wouldn't the shape of the material also need to be a sphere then? Except this, everything else makes sense, thx!