# Standard Deviation of Kinetic Motion

1. Apr 10, 2014

### njmcmu

If thermodynamic temperature can be interpreted as the average kinetic energy in a system, is there a quantity defined as the standard deviation?

For example, lets say you poured some hot water into a cup of cold water. The instant you poured it the standard deviation of the system would be high, and I'm assuming it would lower as it reached thermal equilibrium. Is there a name for this quantity?

2. Apr 10, 2014

### SteamKing

Staff Emeritus
I think 'standard deviation' is only meaningful when you make a series of measurements to determine the properties of a system.

3. Apr 10, 2014

### Staff: Mentor

Better: the average KE per molecule.

The individual molecules have a random distribution of speeds. For example, in an ideal gas:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c3

From this, you can derive the distribution for kinetic energy and find its standard deviation.

4. Apr 10, 2014

### njmcmu

I guess my question could be be asked this way:

Is there a thermodynamic quantity that describes how close or far from thermal equilibrium a system is? And if so, how would this quantity relate to the standard deviation of the energy of the systems constituents?

5. Apr 10, 2014

### dauto

I don't think there is a name for that. Also, keep in mind that temperature really isn't interpreted as the average kinetic energy of particles though that happens to be true for an ideal classic gas model.

6. Apr 11, 2014

### njmcmu

Thank you all for your replies. I actually got my bachelors in physics, but I mostly slept through Thermo . . . both times . . .