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How do I arrive at the density of states which hides inside the expression 2*sqrt(E/pi) * 1/(kB*T)^(3/2) ? I've only seen DOS that have "h" in them.. I want it to contain only E, pi, kB and T.. This is how far I've gotten (using a momentum vector):

V = 4*pi*p^3/3

dV = 4*pi*p^2*dp dV = 4*pi*(2*m*E)*sqrt(m/(2*E))*dE (since p = sqrt(2*m*E) and dp = sqrt(m/(2*E))*dE) dV = 2*pi*(2*m)^(3/2)*sqrt(E)*dE How do I get rid of the m and how do I get in kB and T?

On the same theme:

Is there a DOS-expression D for the ideal gas which will both fit into MB_PDF(E, T) = D * e^(-E/(kB*T)) / Z (where Z normalizes the distribution) as well as giving an extensive entropy S = kB*ln(D) ? It should be the same quantity, right?