double rms speed of molecules of gas

Question

A gas is at 200 K. If we wish to double the rms speed of the molecules of the gas, to what value must we raise its temperature? 

Answer 1

Let v be the rms speed of the molecules. v² is proportional to T where T is the Kelvin temperature.

So if v is to be higher by a factor of 2 , v² will have to be a factor of 4 higher. This means that T will also have to be a factor of 4 higher. Thus T must be raised to 800K