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Disclaimer : I'm not sure that the following is the exact/complete answer to the question but maybe these elements could help. Equilibrium of a system under an external field Let say that you have an open macroscopic system $\Sigma$ (composed of identical particles) which is under the influence of an external time-independant but space-dependant ...


The chemical kinetics of air depend on both how fast you are flying and your altitude. Fortunately, NASA has studied these issues. The figures below are from NASA Report NACA-TN-4359. The predominant chemistry in the stagnation region of an airfoil as a function of flight speed and altitude are shown below: You say $M=7$. If your vehicle is near sea ...


This problem contains a functional form that is very difficult to work with. A numeric integration is one approach that will give an approximate (but good) answer. To do this, the following procedure can be used: 1) Start at pressure P1, and establish a "small" value for dP 2) Use a trial-and-error method to calculate V 3) Multiply V by dP and keep ...


The Fermi energy, $\epsilon_F$, is only equal to the chemical potential, $\mu$, when the Fermi gas is at zero temperature. The Fermi energy basically means, "chemical potential at zero temperature". At any other temperature you could find $\mu$ via one of the standard thermodynamic relations (i.e. as the appropriate derivative of a free energy).

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