Standard Deviation of Kinetic Motion

AI Thread Summary
The discussion explores the concept of standard deviation in the context of kinetic energy and thermodynamic temperature. It questions whether there is a defined quantity that represents the standard deviation of kinetic energy in a system, particularly during thermal interactions, such as mixing hot and cold water. The conversation highlights that while individual molecules exhibit a random distribution of speeds, the standard deviation of their kinetic energy can be derived. It also raises the inquiry of whether a thermodynamic quantity exists that indicates how far a system is from thermal equilibrium. The conclusion suggests that while temperature correlates with average kinetic energy, it may not fully encapsulate the complexities of molecular behavior in non-ideal systems.
njmcmu
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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, let's 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?
 
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I think 'standard deviation' is only meaningful when you make a series of measurements to determine the properties of a system.
 
njmcmu said:
If thermodynamic temperature can be interpreted as the average kinetic energy in a system

Better: the average KE per molecule.

is there a quantity defined as the standard deviation?

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

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