Why root mean square for temperature?

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SUMMARY

The discussion centers on the use of root mean square (RMS) speed rather than mean speed to describe the temperature of a substance. The total kinetic energy of molecules is accurately represented by the equation E=n*(1/2)mv², where v is the RMS speed. This equation fails to hold true if the average speed is used instead of the RMS speed, making RMS a more meaningful metric for understanding molecular behavior and energy distribution.

PREREQUISITES
  • Understanding of kinetic energy equations in physics
  • Familiarity with statistical mechanics concepts
  • Knowledge of molecular motion and temperature relationships
  • Basic grasp of root mean square calculations
NEXT STEPS
  • Study the derivation of the kinetic energy equation E=n*(1/2)mv²
  • Explore the differences between RMS speed and average speed in statistical mechanics
  • Learn about the implications of RMS speed in thermodynamics
  • Investigate the role of molecular motion in temperature measurement
USEFUL FOR

Students of physics, researchers in thermodynamics, and professionals in materials science will benefit from this discussion, particularly those interested in the relationship between molecular speed and temperature.

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I was wondering why it is that when the temperature of something is being described, the root mean square speed of its atoms is used and not simply the mean speed. Why is the RMS more meaningful/useful when describing these things than the mean?

Thanks.
 
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It's simply because the total kinetic energy of the molecules is given by E=n*(1/2)mv^2, where v is the RMS speed. That equation wouldn't work if v were the average speed.
 
ideasrule said:
It's simply because the total kinetic energy of the molecules is given by E=n*(1/2)mv^2, where v is the RMS speed. That equation wouldn't work if v were the average speed.

I guess the question would be better rephrased as: What physical properties of the atoms make it that v being the RMS work as opposed to the average?
 

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