To achieve a root mean square velocity of hydrogen twice its value at STP, the temperature at constant pressure should be increased fourfold.
The root mean square velocity (rms velocity) of gas molecules is directly proportional to the square root of the temperature, as given by the root mean square speed formula:
v_rms = √(3kT/m)
where:
v_rms = root mean square velocity,
k = Boltzmann constant,
T = temperature in Kelvin,
m = mass of the gas molecule.
At constant pressure, according to Gay-Lussac's law, the temperature (T) and rms velocity (v_rms) of a gas are directly proportional. Therefore, to have the rms velocity of hydrogen (H2) twice its value at Standard Temperature and Pressure (STP), the temperature must be quadrupled (2^2 = 4).
This relationship is based on the assumption that other factors, such as molecular mass, remain constant. In this case, the temperature needs to be increased to four times the value at STP for the rms velocity to become twice its STP value.