How many times will the root mean square velocity of nitrogen molecules change if the gas temperature

How many times will the root mean square velocity of nitrogen molecules change if the gas temperature has increased 4 times?

In fact, this task will not be so difficult if you figure it out.

Let’s write the formula for the mean square velocity:

V1sq. = √ * (3 * R * T1 / M)

The second one will have T2, this is the only difference.

We decide further, in the end we will get 2 <V1sq.>

And then we are already entering the home stretch.

<V₂kv> / <V₁kv> = 2 <V₁kv> / <V₁kv>

In the end of such calculations, the answer will be the number 2.

This means that with an increase in the gas temperature by 4 times, the quadratic velocity, in turn, will increase by 2 times. This is the whole task.