The subject of this post is the famous showdown between Eliyahu HaNavi and the prophets of Baal, as described in I Kings chapter 18.
The prophets of Baal came in to the showdown knowing that the best they could hope for was a tie. Their explanation of the ongoing drought was that Baal was being prevented from doing his thing by one or more of the other gods. There was no particular reason to expect Baal to overcome his tormentors today. And they didn't know what Eliahu had up his sleeve. He was the one who got Ahab to organize the showdown. Why now? Why here?
Then Eliyahu framed the issue to be decided in purely monotheistic terms. Verse 21:
וַיִּגַּשׁ אֵלִיָּהוּ אֶל-כָּל-הָעָם, וַיֹּאמֶר עַד-מָתַי אַתֶּם פֹּסְחִים עַל-שְׁתֵּי הַסְּעִפִּים--אִם-יְהוָה הָאֱלֹהִים לְכוּ אַחֲרָיו, וְאִם-הַבַּעַל לְכוּ אַחֲרָיו
Eliyahu let the other side go first in order to have time to set up his "miracle" of fire descending from Heaven. The clues of how he did it are in verse 30:
וַיְרַפֵּא אֶת-מִזְבַּח יְהוָה, הֶהָרוּס
and in verse 38:
וַתִּפֹּל אֵשׁ-יְהוָה, וַתֹּאכַל ... אֶת-הָאֲבָנִים, וְאֶת-הֶעָפָר
Eliyahu chose Mt. Carmel as the location of the showdown because it had a destroyed altar that he could rebuild and because it had access to water (sea water) despite the drought. The "stones" he used to rebuild the altar were special large bricks that he had brought with him for the purpose, bricks whose
main ingredient was quicklime (CaO). The reaction of the quicklime with the water generated enough heat to ignite the wood, and also consumed the "stones".
Calculation: Did the quicklime and the water really get that hot?
The reaction is CaO + H2O -->
Ca(OH)2 , accompanied by the release of 63.7 kilojoules per mole of CaO.
Or per mole of H2O, because of the 1:1 ratio of CaO to H2O.
Is 63.7 kilojoules enough energy to heat a mixture of a mole of quicklime and a mole of water to the ignition temperature of wood?
The molar heat capacity graph at this Web page suggests that a reasonable approximation to use for the molecular heat capacity of quicklime is 45 Joules per mole degree K. The molar heat capacity of water is about 75 Joules per mole degree K. The specific heat of steam is about 36 Joules per mole degree K. The heat of vaporization of water is 40.65 kilojoules per mole. That leaves 23.05 kilojoules to heat the
quicklime and the water/steam. Assuming an initial temperature of 25C, the energy needed to get to the boiling point of the water is
75 degrees K * 120 Joules/mole-degree-K = 9 kilojoules
which leaves about 14 kilojoules to heat the steam and the quicklime. So the final temperature is 100 degrees C plus
14 kilojoules / 0.081 kilojoules per mole-degree-K = 173 degrees K
So the altar attains a temperature of about 273 degrees C. According to this Web page the "ignition temperature of various woods" is 190 - 260 degrees C. After the wood starts burning, it gets hotter just by burning. Eliyahu had lots of time on his hands at Wadi Krit and in Zarefat to experiment with what kind of wood works best and with what to use to coat a quicklime brick to stabilize it against reacting with the moisture in the air.
