Coal Fire And Nice Days

The problem is Lignite (a form of coal) has a density of only $801\,kgm^{-3}$ which would mean,

$v_{boom\,lignite}=3.4354*\cfrac{801}{6}=458.63\,ms^{-1}$

and

$T_{458}=\cfrac{458.63^2*12.0107*10^{-3}}{3*8.3144}=101.28\,K$

Lignite will spontaneously ignite at $101.28-273.15=-171.87\,^oC$!  What happened?  Apparently, lignite low density value is due to bulk (air space) and is not structural.  The quoted density value is bulk density.

In the case of Anthracite, another form of coal, with a density value of $1506\,kgm^{-3}$,

$v_{boom\,anthracite}=3.4354*\cfrac{1506}{6}=862.29\,ms^{-1}$

and

$T_{862}=\cfrac{862.29^2*12.0107*10^{-3}}{3*8.3144}=358.03\,K$

It will ignite at $84.88\,^oC$

And bituminous coal of a density $1346\,kgm^{-3}$,

$v_{\small{boom\,bituminous}}=3.4354*\cfrac{1346}{6}=770.67\,ms^{-1}$

and

$T_{770}=\cfrac{770.67^2*12.0107*10^{-3}}{3*8.3144}=285.99\,K$

It will ignite at $12.84\,^oC$!  For miners, mining this type of coal in tunnels or open pits, this is the temperature at which the ore starts to emit poisonous $CO$ gas.  It does not ignite into an open flame, but the carbon begins to react with atmospheric oxygen $O_2$ and produce $CO$.

And another quoted value of density for coal at $1400\,kgm^{-3}$

$v_{\small{boom\,brown}}=3.4354*\cfrac{1400}{6}=801.59\,ms^{-1}$

and

$T_{770}=\cfrac{801.59^2*12.0107*10^{-3}}{3*8.3144}=309.40\,K$

It ignites at $36.25\,^oC$

Crystalline (structural) density should be used and not bulk density in the calculations for $v_{boom}$ and $T_{v\,boom}$.

Such fire will linger around $T_{v\,boom}$, unless it is cooled below this temperature.  Beyond ignition, combustion in the air generates most of the raise in temperature.

...if you have a coal fire to put out.  Go put out the fire, don't have a nice day.