All Problems

Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.90

Find the fraction of molecules whose velocity projections on the xx axis fall within the interval from vxv_{x} to vx+dvx,v_{x}+d v_{x}, while the moduli of perpendicular velocity components fall within the interval from vv_{\perp} to v+dv.v_{\perp}+d v_{\perp} . The mass of each molecule is m,m, and the temperature is Tˉ\bar{T}.

Reveal Answer
dN/N=(m2πkT)3/2emv2/2kT2πvdvdvxd N / N=\left(\frac{m}{2 \pi k T}\right)^{3 / 2} \mathrm{e}^{-m v 2 / 2 k T} 2 \pi v_{\perp} d v_{\perp} d v_{x}