Chapter 18, Problem 87E

(a)

To determine

The number of molecules with speeds in the finite interval $v$ to $v+dv$ is $\Delta N=N{\displaystyle \underset{v}{\overset{v+\Delta v}{\int }}f\left(v\right)dv}$ in a gas of $N$ molecules.

(b)

To determine

The number of molecules within speeds within $\Delta v=20\text{m/s}$ of $v_{\text{mp}}$ and express the answer as the multiple of $N$.

(c)

To determine

Repeat part (b) for speeds within $\Delta v=20\text{m/s}$ of $7v_{\text{mp}}$.

(d)

To determine

Repeat part (b) and (c) for a temperature of $600\text{K}$.

(e)

To determine

Repeat part (b) and (c) for a temperature of $150\text{K}$.

(f)

To determine

Analysis of results obtained from the graph between between the distribution function and the function of temperature.