Question

The thermodynamic temperature of an ideal gas is raised from T to 2T. Which quantity must be
doubled?
A.
the root-mean-square speed of the molecules
B.
the square of the mean speed of the molecules
C. the mean speed of the mole
D.
the mean-square speed of the molecules
​

Answer 1

Root mean square speed, v

$v = \sqrt{\frac{3RT}{M} }$

M= mass, R= universal gas constant, T = temperature.

v² ∝ T

So, if Temperature increases from T to 2T, v will increase from v² to 2v²

i.e. the square of the root mean square speed of the molecules must be doubled.

Option B)