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6

How opaque is that -- would we be able to see a couple of meters, some kilometers, or nothing at all? The photosphere of our sun is somewhere on the order of 500 km thick. For a quick ballpark, you can imagine an exponential decrease in the transmission of light which about this characteristic thickness. It might be a little less, but it's still ...


3

The question of AdS (in)stability is indeed a hot topic in current research of the AdS/CFT correspondence. It is a field that ties together many interesting subjects: Gravity in AdS (i.e a confining box), thermalization in QFTs, the theory of non-linear differential equations and their perturbative treatment, turbulence etc. This explains the explosion of ...


2

Well, I can give you a definitive answer to Q1, but my answer to Q2 would only be educated speculation. Perhaps some of the astrophysicists on here can be more help with that one. However, before I tackle Q1, a very important disclaimer: Temperature is a measure of the average kinetic energy of the particles of an object, and cannot be used all by itself ...


2

To answer your question first we need to know why do we need quantum mechanics in thermodynamics: In Quantum mechanics you can attribute a wave function(to be precise wave-packet) to a particle. . At high temperatures particles can be pictured as billiard balls because their size is much smaller compared to interparticle distance. But as the gas cools down ...


1

For the record, it might be a partially blown head gasket letting water flow from the coolant channels, into the combustion chambers, and out the exhaust. A lot of water flowing out of the exhaust isn't normal.


1

I think this should be roughly correct. If you want to also roughly estimate the difference that internal heat, tides and atmosphere (the Earth's) would have had, you can look at the moon, which is the same distance from Titan but has an average surface temperature of $268K$. So your error is about $20K$ for estimating earth's temperature from Titan's. ...


1

The general answer seems to be that everything you know is correct and we cannot have a material with a negative bulk modulus. But we can have materials with a negative incremental bulk modulus. In other words, I can't make a material that will always expand when you try to compress it. But I can make one that will compress for a little while, then expand ...


1

Following is computation of $E[(\sigma_a - E[\sigma_a])(\sigma_b-E[\sigma_b])]$: $E[(\sigma_a - E[\sigma_a])(\sigma_b-E[\sigma_b])]=\\ E[\sigma_a\sigma_b-\sigma_aE[\sigma_b]-E[\sigma_a]\sigma_b+E[\sigma_a]E[\sigma_b]]=\\ E[\sigma_a\sigma_b]-E[\sigma_a]E[\sigma_b]-E[\sigma_a]E[\sigma_b]+E[\sigma_a]E[\sigma_b]=\\ E[\sigma_a\sigma_b]-E[\sigma_a]E[\sigma_b]$ ...


1

The key question is "Per mole or per gram?" Because the both values can be found tabulated as "specific heat" in various sources. Perhaps it would be useful to distinguish "molar specific heat" from "specific heat per unit mass". You seem to be using the intuition for the molar quantity, so if the table is by mass, the answer is simply that you need more ...



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