Question

Using the function of molecular speed distribution Maxwell - Boltzmann for an ideal gas mono-atomic, given by: $f(u,T) = 4\pi N(\frac{m}{2\pi kT})^{\frac{3}{2}} u^{2}e^{\frac{-mu^{2}}{2kT}}$ and the formula for the gaussiano integral and its n momentums are given by:

$\int_{0}^{\,\infty } e^{-\alpha x^2}dx = \frac{1}{2}\sqrt{\frac{\pi}{\alpha }}$

$\frac{d^{n}}{d\alpha ^{n}}\int_{0}^{\infty } e^{-\alpha x^2}dx = \frac{\sqrt{\pi}}{2}\frac{d^{n}}{d\alpha ^n}\alpha ^{-\frac{1}{2}}$

$\int_{0}^{\infty }xe^{-\alpha x^2} dx = \frac{1}{2\alpha }$

$\frac{d^n}{d\alpha ^n}\int_{0}^{\infty } xe^{-\alpha x^2}dx = \frac{1}{2}\frac{d^n}{d\alpha ^n} \alpha ^{-1}$

Find an expresion in terms of m, T, N and k, for:

the average molecular speed, the average speed square, the deviation "standard", the average molecular kinetic energy, and the pressure exerted by the gas.

Answer 1

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