The oxygen in a room ( ) is at

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Kinetic theory and transport in gases · Kinetic theory and transport in gases

Thermal Physics, Ch Temperature, pressure and the kinetic theory of gases

Problem

The oxygen in a room (M=32.0 g mol−1M = 32.0\,\mathrm{g\,mol^{-1}}) is at T=300 KT = 300\,\mathrm{K}. Treat it as a dilute ideal gas with the Maxwell-Boltzmann speed distribution. ((a)) Find the most probable speed vpv_p. ((b)) Estimate the fraction of the molecules with speeds between 390390 and 400 m s−1400\,\mathrm{m\,s^{-1}}, treating f(v)f(v) as constant across that narrow range. ((c)) The fraction of molecules faster than v=xvpv = xv_p is 2xπ e−x2+2π∫x∞e−u2 du.\frac{2x}{\sqrt\pi}\,e^{-x^2} + \frac{2}{\sqrt\pi}\int_x^\infty e^{-u^2}\,\mathrm{d}u. Using the tabulated value ∫1∞e−u2 du=0.1394\int_1^\infty e^{-u^2}\,\mathrm{d}u = 0.1394, find the fraction of the molecules faster than vpv_p and the fraction slower. Does the peak of the curve split the molecules into two equal halves? Use kB=1.381×10−23 J K−1k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}} and NA=6.022×1023 mol−1N_A = 6.022\times10^{23}\,\mathrm{mol^{-1}}.

Browse the problem library