Answer
$P = \frac{1}{3}~\rho~v_{rms}^2$
Work Step by Step
$\overline{KE} = \frac{3}{2}~kT$
$\frac{1}{2}~m~v_{rms}^2 = \frac{3}{2}~kT$
$\frac{1}{2}~m~v_{rms}^2 = \frac{3}{2}~\frac{P~V}{N}$
$\frac{1}{3}~m~v_{rms}^2 = \frac{P~V}{N}$
$P = \frac{1}{3}~(\frac{N~m}{V})~v_{rms}^2$
$P = \frac{1}{3}~\rho~v_{rms}^2$
