PrepZii

mixed

Translational KE and Molecular Speeds

The source lists translational kinetic energy of gas, RMS speed, average speed, and most probable speed.

K=\frac{1}{2}M\langle V^2\rangle=\frac{3}{2}PV=\frac{3}{2}nRT

\langle V^2\rangle=\frac{3P}{\rho}

V_{rms}=\sqrt{\frac{3P}{\rho}}=\sqrt{\frac{3RT}{M_{mol}}}=\sqrt{\frac{3KT}{m}}

\bar V=\sqrt{\frac{8KT}{\pi m}}=1.59\sqrt{\frac{KT}{m}}

V_p=\sqrt{\frac{2KT}{m}}=1.41\sqrt{\frac{KT}{m}}