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The derivation of ideal gas equation from Hamilton's equations will take the same procedure as what you have seen in Wikipedia. Since you said you haven't understood the way in which the equation is derived I will give you a step by step explanation on it. So we have a system of perfect gas molecules. Of course they are non-interacting. We are going to ...


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Short answer: It can be compressed, due to extreme pressure, but only slightly. The Wikipedia page on the Mariana Trench says that the seawater density is 4.96% greater there than at the surface. Also refer to Hydrostatic pressure - doesn't density vary with depth?. Further explanation (and assuming everything you currently know about water is that ...


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Liquids are compressible but in lots of cases the fact that the volume of water decreases by about fifty parts per million for an increase in pressure of one atmosphere can be ignored. A similar approximation is also often made about the compressibility of solids.


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Well, contrary to what Lemon said, internal energy is sum of ALL energy of constituting particles related to their DISORDERED motion only. To prove my statement, look out for the derivation of formula for internal energy for an IDEAL gas, and the derivation for value of C(molar heat capacity at constant volume) henceforth. Now coming to your question, since ...


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In kinetic theory, we can estimate $$ \eta \sim n\bar{p}l_{p} $$ and $$ \kappa \sim (c_p/m) \bar{p} l_{q} $$ where $\bar{p}$ is the mean momentum and $l_p$ and $l_q$ are the mean free paths for momentum and energy transport. The statement that the Prandtl number is of order 1 is then simply the observation that the two mean free paths are comparable. In a ...


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Yes, these are three different values. But why do you call it a problem? This is just so. Take for example three numbers: 1, 1 and 4. The average of the squares (energy) is 6, the square of the average is 4, and the square of the most probable value is 1. There is no problem :)



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