Question

Calculate the temperature at which r.m.s velocity of gas molecules become double .

Answer 1

Theory

RMS velocity

it is used to predict how fast gas molecules are moving at a given Temperature.

$v = \sqrt{ \frac{rt}{m} }$

Question

Calculate the temperature at which r.m.s velocity of gas molecules become double ?

solution

let at temperature t , RMS velocity is v.

and at temperature x,RMS velocity is doubled means 2 v.

therefore ;

$v = \sqrt{ \frac{3rt}{m} } \: \: \: ...(1)$

and ,

$2v = \sqrt{ \frac{3rx}{m} } \: \: \: ...(2)$

divide equations (1)& (2)

then ,

$\frac{v}{2v} = \sqrt{ \frac{t}{x} }$

$\frac{1}{2} = \sqrt{ \frac{t}{x} }$

$\frac{t}{x} = \frac{1}{4}$

$x = 4t$

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