A sealed glass cell holds molecular oxygen ( ) as a dilute ideal gas in thermal…

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

A sealed glass cell holds molecular oxygen (M=32.0 g mol−1M = 32.0\ \mathrm{g\,mol^{-1}}) as a dilute ideal gas in thermal equilibrium at a single temperature TT. An experiment measures the distribution of one Cartesian component of molecular velocity and the data fit the form f(vx)=C e−bvx2,b=5.0×10−6 s2 m−2,f(v_x) = C\,\mathrm{e}^{-b v_x^2},\qquad b = 5.0\times10^{-6}\ \mathrm{s^2\,m^{-2}}, with vxv_x in m s−1\mathrm{m\,s^{-1}} and f(vx) dvxf(v_x)\,\mathrm{d}v_x the fraction of molecules with xx-component of velocity in dvx\mathrm{d}v_x. ((a)) Use the Gaussian integral to find CC, with its unit. ((b)) Find the temperature TT of the gas. ((c)) Find the most probable, mean and root-mean-square speeds and state their ordering. 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}}.

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