Theory of RMS Speed Formula Explained | Understanding Vrms = √(3RT/M)

[l33t_V]

Hello all,

I would like to know what is the theory behind the formula of the rms speed,
Vrms = root(3rt/M).

Thank you

 

[jtbell]

http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kinthe.html

http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kintem.html (this page has your equation)

 

[astrokreng]

for your question. The theory behind the rms speed formula is derived from the kinetic molecular theory of gases, which states that all gas molecules are in constant random motion and have a distribution of speeds. The root-mean-square (rms) speed is a way to calculate the average speed of gas molecules in a given sample.

The formula Vrms = √(3RT/M) is a combination of the ideal gas law (PV = nRT) and the definition of average speed (Vavg = √(8RT/πM)). It takes into account the temperature (T), which is related to the average kinetic energy of the gas molecules, and the molar mass (M) of the gas molecules.

The √(3RT/M) part of the formula represents the average speed of a single gas molecule, while the √(8RT/πM) part represents the average speed of all gas molecules in the sample. By taking the square root of the average of these two values, we get the rms speed, which is a more accurate representation of the overall speed of the gas molecules.

In summary, the rms speed formula is derived from the kinetic molecular theory and takes into account the temperature and molar mass of gas molecules to calculate the average speed of a gas sample. It is a useful tool in understanding the behavior of gases and can be applied in various scientific and engineering fields. I hope this explanation helps to clarify the theory behind the formula.