Average Kinetic Energy

[andafoo]

Does anyone know where the equation:

KEavg = (3/2)RT

For the average kinetic energy of a fluid? Derivations anyone ... if simple?

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[HawkeyePostOp]

if u is root mean square speed of the fluid with molar mass M,
Avagadro's number N,

then KE is(M/2N)u^2 = 3RT/2N

remove N and you have the average ke of a particle = (3/2)RT

It's a waste of time unless you're already scoring 13 on PS

 

[andafoo]

if u is root mean square speed of the fluid with molar mass M,
Avagadro's number N,

then KE is(M/2N)u^2 = 3RT/2N

remove N and you have the average ke of a particle = (3/2)RT

It's a waste of time unless you're already scoring 13 on PS

Thanks, I know it rarely shows up, but I didn't want to memorize the equation ... got enough on the brain.

Although the derivation does not make sense to me at this point.

you are replacing v with the RMS velocity (average velocity)
you are also replacing the 'm' with M/N, which is the mass per particle...

how does that result in the gas constant and temperature?

It looks like it's really close, but I just don't see that 1 intermediate step.

 

[HawkeyePostOp]

u = (3kNT/M)^(1/2)