Question $1$: Use $F(v)dv$ function for $v$ to find $($:$v^3$:$)$ for ideal gas molecule $($show $($:$v^3$:$)$ in terms of $($:$v$:$).$

$F($:$v$:$)dv=4v^2(\frac{m}{2kT}{)}^{\frac{3}{2}}$exp$(-\frac{m{v}^2}{2kT})$

$($:$v$:$)=(\frac{8kT}{m}{)}^{\frac{1}{2}}$