Word Count : 413

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To determine the average speed and root mean square (rms) speed of a molecule in a Maxwellian gas, we start with the given Maxwell-Boltzmann speed distribution: \[ dN_v = 4\pi N \left( \frac{m}{2\pi k_B T} \right)^{3/2} v^2 e^{-\frac{mv^2}{2k_B T}} dv \] where: - \( N \) is the total number of molecules, - \( m \) is the molecular mass, - \( k_B \) is Boltzmann’s constant, - ____ ___ _____ ___ ________.
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