I read the tutorial that says Also, as T → 0, so do T^3/2 but i did not understand this argument.
In this formula, where does T come from to the power of 3 divided by 2?
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\$\begingroup\$ (a) Ideal gas law via the Drude model for electrons. (b) The assumption of available states to a monatomic gas [unpaired electrons, which only get paired if they become Cooper pairs and then the statistics are different anyway] in 3 dimensions with \$\frac{kT}{2}\$ for each (\$\frac32\$ already arriving.) (c) The assumption of an adiabatic process -- no heat exchange. You don't even need a semiconductor book to find \$T^{^\frac32}\$. It's pretty much in any good statistical thermodynamics book. I could develop it, but there are already too many such texts around. Kittel, 1969, for example. \$\endgroup\$– jonkCommented May 8, 2022 at 16:57
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\$\begingroup\$ What exactly are you wanting to know about this? \$\endgroup\$– jonkCommented May 8, 2022 at 17:46
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1 Answer
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Based on your quoted passage, the derivation of the formula is given in Ref.(1). As long as the power of T is greater than 1, the expression will get smaller and smaller as T approaches 0 which leads to the conclusion that the expression itself will also approach 0. Note that a number less than 1 gets smaller when it is cubed. Taking the square root only slows down that process. Thus the process of cubing and then taking a square root of T results in a smaller number when T is less than 1.
