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velocity of gas and temperature

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echoyjeff222

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i know that when temp is doubled, the KE doubles and therefore velocity goes up by sqrt2.

Can I show this through the root mean squared formula with vrms = sqrt3RT/m as well, or is not not a valid way to show it?
 

swivelj

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The Vrms formula shows you the same relationship you just described in the KE expression.

Look at the expression for Vrms

Vrms = sqrt 3RT/M

if you double T ......... R is a constant and doesnt change and neither does the mass of the gas so......

Vrms = sqrt (2T)

so just like the KE expression it shows velocity goes up by sqrt 2 if temperature doubles (2T).



This is why you can also use this exression to compare the same gas at different temps, if we know the velocity at one of the temps.

v1/v2 = sqrt T1/T2


v1 is directly related to the sqrt of T1
v2 is directly related to the sqrt of T2
 
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