1 answer

Use the Maxwell-Boltzmann distribution of speeds to estimate the fraction of N2 molecules at 392 K...

Question:

Use the Maxwell-Boltzmann distribution of speeds to estimate the fraction of N2 molecules at 392 K that have speeds in the range 200. – 210. m·s−1. Hint: The fraction of molecules with speeds in the range v to

(v + dv)

is equal to

f(v)dv,

Please show entire integration for boltzmann formula.


Answers

2 Maxwell -Boltzmann lig speed distribution in velocity distributio lawi- consider an ideal gas in a container. Assumptions:As, volume elements dux, duy, duz located at the tip of we take o fixed = fixed NF. (W) = fired idNF (~)Jeo [Nf (wxdfwy) + (WJux taux=0 df (x) Const Integrate enfway=-& va tena -. in five cavab a flux) = te a flwy) =ée- five) - Ae- az = N(ANA, e-q (= NA e-Bv2 duxdry drez = NA e-Buz 0, NA? e-Bv² u2gu sine dede do 2 sirodos ad INV 41NA² e-Bu speed distribution law. ; No, beNow Average kinetic energy per molecule Boltzmann constant <tmay= 3 KT - Absolute temp.</p><p>=> { m<w2y = 2KT = m.BKT :. 0 $ - - -- 41. let) = AT. - ZRT 2TRT = 4*3.14 « la 10.028 kg moll 2x3.14x8.31434 mol (3926) $2 - 0,028kg mot 2x8.319 3 motax (392K) l

.

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