Question

If the absolute temperature of a gas is quadrupled, what happens to the root‑mean‑square speed of the molecules? Nothing happens to the rms speed. The new rms speed is 16 times the original rms speed. The new rms speed is 4 times the original rms speed. The new rms speed is 2 times the original rms speed. The new rms speed is 1/4 the original rms speed.

Answer 1

The new rms speed is 2 times the original rms speed.

Step-by-step explanation:

The root‑mean‑square speed, rms, is related to temperature, , by the formula

`_(rms)`= √3 / ℳ

For a given gas,

`_(rms)` ∝ √

or

`_(rms,2)` /
`_(rms,1)` = √
`_(2)` /
`_(1)`

In this case, is quadrupled.

√4 = 2

The new rms speed is 2 times the original rms speed.