Final answer:
To triple the rms speed of the gas molecules, we need to raise the gas's temperature to 9 times its initial temperature.
Step-by-step explanation:
To triple the rms speed of the gas molecules, we need to find the new temperature. The rms speed of gas molecules is directly proportional to the square root of the temperature. Let T be the initial temperature. To triple the rms speed, we need to find the new temperature, T'. According to Charles's law, at a constant pressure, the volume of a gas is directly proportional to its temperature.
V = k * T,
where V is the volume and k is a constant.
Since we want to triple the rms speed, we have:
√T' = 3 * √T
By squaring both sides of the equation, we get:
T' = 9 * T
Therefore, the gas needs to be raised to a temperature 9 times the initial temperature to triple the rms speed of its molecules.