# Help with root mean square speed

1. Jul 19, 2006

### nithin

hi guys i gota question in chemistrygas laws , i thought about it and am still confused ~~~~~~~~~~~ what does the area under a number of molecules against speed of gas represent????? it is to do with root mean square speed ... i thought that it might be the average kinetic energey but it seems unlikely to be so ... just for reference http://wine1.sb.fsu.edu/.../ Gases/Kinetic/Gases08.htm

2. Jul 19, 2006

### vijay123

3. Jul 19, 2006

### nithin

number of molecules??? why?

4. Jul 19, 2006

### Gokul43201

Staff Emeritus
1. That URL is incomplete - please fix it.

2. Are you refering to the Boltzmann distribution of molecular speeds? The y-axis represents the number of molecules whose speeds lie within some v and v+dv.

3. For any collection of particles (eg:molecules), you can define what is known as a molecular distribution function, f(r,v,t) which is the mean number of molecules whose center of mass at time t is found between r and r+dr and whose velocities lie between v and v+dv. The y-axis of the Boltzmann curve is like the time averaged distribution independent of position, $n(v) = (1/T) \int_0^T dt \int_{box} d^3r f(r,v,t)$

4. The mean square velocity is simply $(1/T) \int dt \int d^3r \int d^3v f(r,v,t) v^2$. The RMS velocity is the square root of this number.

5. The total area under the Boltzmann curve $(1/T) \int dt \int d^3r \int d^2v f(r,v,t)$ is the number of molecules that can be found at any position, possessing any velocity, ie: the total number of molecules in the box.

6. The area under the curve between two speeds v1 and v2 represents the total number of molecules having speeds between v1 and v2.

Last edited: Jul 19, 2006