Chapter 19, Problem 19.72E

Interpretation Introduction

Interpretation:

The graphs of $g_{\text{x}}$ versus $v_x$ and $G\left(v\right)$ versus $v$ are to be compared and the similarities and differences in the graphs are to be stated.

Concept introduction:

The probability distribution function of the velocities of the gas molecules in each dimension is given by $g_x\left(v_x\right)$, $g_y\left(v_y\right)$ and $g_z\left(v_z\right)$. This is a vector quantity. This probability function in the range of $-\infty$ to $+\infty$ is represented by,

${\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}{g}_x\left(v_x\right)d{v}_x}=1$

The Maxwell-Boltzmann distribution is given by,

$G\left(v\right)dv=4\pi {\left(\frac{m}{2\pi kT}\right)}^{3/2}{v}^2\cdot e^{-m{v}^2/2kT}dv$

This distribution depends on the mass of the particle and absolute temperature.