Chapter 3, Problem 3.15E

(a)

Interpretation Introduction

Interpretation:

Temperature of each curve of distribution of speeds for ${\text{N}}_{\text{2}}$ below has to be determined.

Concept Introduction:

Maxwell distribution curve shows the different fraction of gas molecules moves with different speeds. It also shows that heavy molecules have slow speed while lighter molecules have faster speeds. The formula to calculate faction of gas molecules with given speed $\left(v\right)$ at any instant of time is as follows:

  $f\left(v\right)=4\text{π}{\left(\frac{M}{2\text{π}RT}\right)}^{\text{3/2}}{v}^2{e}^{-M{v}^2\text{/2RT}}$

(b)

Interpretation Introduction

Interpretation:

Value of $v_{\text{rms}}$ has to be determined.

Concept Introduction:

Root mean square speed is square root of average value of square of molecular speeds of molecules of gas. It includes molecular weight and temperature, both of which affect kinetic energy of a gas. It is denoted by $v_{\text{rms}}$. The expression for $v_{\text{rms}}$ is as follows:

  $v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

Here,

$R$ is gas constant.

$T$ is absolute temperature of gas.

$M$ is molecular weight of gas.