Standard Deviation of Kinetic Motion

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Discussion Overview

The discussion revolves around the concept of standard deviation in the context of kinetic energy and thermodynamic temperature, particularly in relation to systems approaching thermal equilibrium. Participants explore whether a quantity analogous to standard deviation exists for describing the distribution of kinetic energy in a system.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions if there is a defined quantity analogous to standard deviation for kinetic energy in a system, particularly as it approaches thermal equilibrium.
  • Another participant argues that 'standard deviation' is meaningful only when a series of measurements is made to determine system properties.
  • A different participant suggests that the average kinetic energy should be considered per molecule and mentions that individual molecules have a random distribution of speeds, referencing the derivation of kinetic energy distribution and its standard deviation in an ideal gas.
  • One participant rephrases the original question to inquire about a thermodynamic quantity that indicates how far a system is from thermal equilibrium and its relation to the standard deviation of the energy of the system's constituents.
  • Another participant expresses skepticism about the existence of a specific name for such a quantity and notes that temperature is not strictly interpreted as the average kinetic energy of particles, despite being true for ideal gases.
  • A participant shares their background in physics, indicating a personal connection to the topic but also a lack of engagement with thermodynamics during their studies.

Areas of Agreement / Disagreement

Participants express differing views on the meaningfulness of standard deviation in this context, with some questioning its applicability and others exploring its potential relevance. There is no consensus on whether a specific thermodynamic quantity exists that describes the distance from thermal equilibrium.

Contextual Notes

Participants acknowledge the limitations of their discussion, including the dependence on ideal gas models and the lack of clarity regarding definitions and assumptions about temperature and kinetic energy.

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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