A

The statement refers to the kinetic theory of gases, which relates the average speed of gas molecules to temperature.
According to the kinetic theory, the mean speed \( \bar{v} \) of the molecules of a gas is given by the formula:
\[ \bar{v} = k \sqrt{T} \]
where \( k \) is a proportionality constant and \( T \) is the absolute temperature in Kelvin.
This shows that as the temperature increases, the mean speed of the molecules also increases in proportion to the square root of the temperature. Therefore, the statement is correct.