Relation between kinetic energy and temperature

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Discussion Overview

The discussion centers around the relationship between kinetic energy and temperature, specifically exploring the origin of the factor of 3/2 in the equation relating them. The scope includes theoretical aspects, mathematical reasoning, and references to the equipartition theorem and kinetic theory.

Discussion Character

  • Technical explanation, Mathematical reasoning, Conceptual clarification

Main Points Raised

  • Some participants inquire about the origin of the factor 3/2 in the equation relating kinetic energy and temperature.
  • One participant suggests that the factor of 3 arises from the three spatial dimensions in which a particle can move, with each dimension contributing kt/2 to the total kinetic energy.
  • Another participant explains that the three translational degrees of freedom contribute 1/2kt each to the total energy, referencing the equipartition theorem.
  • A different perspective is presented, indicating that the 3kT/2 can be derived by equating two ideal gas equations, one derived experimentally and the other from kinetic theory.

Areas of Agreement / Disagreement

Participants express various viewpoints on the derivation of the factor 3/2, with no consensus reached on a single explanation. Multiple competing explanations remain present in the discussion.

Contextual Notes

The discussion involves assumptions related to the ideal gas behavior and the applicability of the equipartition theorem, which may not hold in all conditions.

johnathon
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Where does the 3/2 come from?
\frac{1}{2} mv^2 = \frac{3}{2} kT
 
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A particle can move in any of three directions (that's where the 3 comes from), with kt/2 being the kinetic energy carried by motion on each the x,y or z dimensions.
This link gives a short and sweet bit of book work. That Hyperphysics site is good for many things, actually.
 
johnathon said:
Where does the 3/2 come from?
\frac{1}{2} mv^2 = \frac{3}{2} kT
There are three translational degrees of freedom, each contributing 1/2kt to the total energy. This from the equipartition theorem.
 
Taking it back a step the 3kT/2 can be found by equating the two ideal gas equations,one being obtained experimentally(PV=RT) the other being obtained theoretically using kinetic theory(PV=Nmc bar squared/3)
 

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