At what temperature will the root mean square velocity of molecules of a gas be twice the root mean square velocity at zero degree Celsius at what temperature 1.5 times?

Dear Student,

Please find below the solution to the asked query: The equation for the rms speed is,

Vrms=3RTm

So, at T = 300 K, rms speed is V1, then let the temperature T2, where the rms speed is 2V​1.

V2V1=3RT2m3RTm ⇒ 2VV=T2300 ⇒ T2=1200 K

Let the temperature T3, where the rms speed is 1.5 times to the rms speed at T = 300 K.

V3V1=T3300 ⇒ 1.5VV=T3300 ⇒ T3=2.25×300⇒T3=675 K