Answer to Question #160592 in Molecular Physics | Thermodynamics for Carty

Question

Explain what is mearnt by the root mean square velocity of the molecules of a gas.

Answer 1

By definition, the root mean square velocity (speed) is (https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution#Typical_speeds):

$$v_{rms} = \left( \int_0^{\infty }v^2f(v)dv \right)$$

where

$$f(v) = \left(\frac{m}{2 \pi kT}\right)^{3/2}\, e^{ - \frac{mv^2}{2kT}}$$

is the Maxwell–Boltzmann distribution. The value of root mean square velocity is:

$$v_{rms} = \sqrt{\dfrac{3RT}{M}}$$

where $R$ is the gas constant, $T$ is the absolute temperature of the gas, and $M$ is the molar mass of the gas.