Relation between kinetic energy and temperature

johnathon

Where does the 3/2 come from?
[tex]\frac{1}{2} mv^2 = \frac{3}{2} kT [/tex]

sophiecentaur

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.

Doc Al

Quote by johnathon

Where does the 3/2 come from?
[tex]\frac{1}{2} mv^2 = \frac{3}{2} kT [/tex]

There are three translational degrees of freedom, each contributing 1/2kt to the total energy. This from the equipartition theorem.

Dadface

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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johnathon	Relation between kinetic energy and temperature Tweet Where does the 3/2 come from? [tex]\frac{1}{2} mv^2 = \frac{3}{2} kT [/tex]

sophiecentaur Recognitions: Gold Member Science Advisor	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.

Dadface Recognitions: Gold Member	Relation between kinetic energy and temperature 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)