If the absolute temperature of a gas is tripled, what happens to the root‑mean‑square speed of the molecules?
a. nothing happens to the rms speed.
b. the new rms speed is 9 times the original rms speed.
c. the new rms speed is 3 times the original rms speed.
d. the new rms speed is 1.732 times the original rms speed.
e. the new rms speed is 1/3 the original rms speed.

D. The new rms speed is 1.732 times the original rms speed.

Explanation:

The expression for the root mean square speed is:

R is Gas constant having value = 8.314 J / K mol  

M is the molar mass of gas

T is the absolute temperature

As seen from the formula, root mean square speed is directly proportional to the square root of the absolute temperature.

So,

Given, absolute temperature of a gas is tripled, so, the new rms speed will be √3 (1.732) of the original.

Hence, the correct option is:- D. The new rms speed is 1.732 times the original rms speed.

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