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I am reading "What if?" article https://what-if.xkcd.com/20/ and I'm interested in it's scientific background. Mr. Munroe writes:

As it [the meteor] falls, it compresses the air in front of it. When the air is compressed, it heats it up. (This is the same thing that heats up spacecraft and meteors—actual air friction has little to do with that.) By the time it reaches the ground, the lower surface will have heated to over 500℃, which is enough to glow visibly.

How can one make such estimation? I wanted to use PV = nRT, but I don't know the volume and the difference in pressure. I tried to sum up all the kinetic energy of all air molecules of the air, bumping into the meteor, but the answer is nowhere near. Does anyone have an idea? Such an interesting problem.

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    $\begingroup$ The ideal gas equation doesn't work on meteors. $\endgroup$ – Soba noodles Sep 23 '15 at 21:53
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    $\begingroup$ There are different ways to model this. One of the best is the real gas model. Looking at it a different way, a computational approach that's interesting is CEA. $\endgroup$ – HDE 226868 Sep 23 '15 at 22:41
  • $\begingroup$ Related: (1); Useful links: (a), (b), you may google the rest. $\endgroup$ – Soba noodles Sep 23 '15 at 22:54
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Ram Pressure produces a large amount of atmospheric drag force, by the compression of the air located ahead of the meteor. It's equation is:

P = $\rho$v $^2$

P is the pressure, $\rho $ is the fluid density and v is the velocity of the meteor.

The remainder of your answer might be found here, Drag and Heat, so rather than duplicate that, I will ask you read it and hope it helps you.

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It is true that the most contribution to heat comes from compressing the air. The temperature of a falling meteor was in fact in my aerodynamics II exam where I had to predict its temperature using shockwaves. According to my estimation it was about 10,000 K. You need a proper understanding of compressible air flows in order to answer this question. And I know a little about it.

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The most significant contribution to the heat generation is the the exothermic reaction of iron in the meteorite with atmospheric oxygen and nitrogen. The oxides and nitrates that form at the leading entry surface are not uniform. They will distribute themselves so that there is the greatest possible entropy among them. This will be another ongoing process. So there will be heat generated from molecules avoiding any definable order among themselves. Furthermore as the oxygen and nitrogen are heated under pressure a great deal of nitric and nitrous acids will form with help from water vapor in the air....which will react further with the iron, contributing another exothermic reaction. Unless that meteorite is made of some highly unreactive substance(s) calculating the heat it will generate or temperature it will attain is going to be a really tough problem.

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