A fixed volume of an ideal gas is heated - AQA - A-Level Physics - Question 8 - 2022 - Paper 2

To determine which quantities double when the Kelvin temperature of an ideal gas doubles, we can refer to the ideal gas law and related physical principles.

1. RMS Speed of Molecules: The root mean square (RMS) speed of gas molecules can be expressed with the formula:

   $v_{rms} = ext{sqrt}\left( \frac{3RT}{M} \right)$

   Here, $v_{rms}$ is the RMS speed, $R$ is the gas constant, $T$ is the absolute temperature in Kelvin, and $M$ is the molar mass of the gas. When the temperature $T$ doubles, the RMS speed also doubles.

2. Density of the Gas: The density of the gas $ho$ is given by the formula:

   $\rho = \frac{PM}{RT}$

   Where $P$ is the pressure. At constant volume, if the temperature doubles, the pressure will also double (assuming an ideal gas). This means that the density does not necessarily double.

Thus, the correct answer indicating that both quantities that double when the temperature doubles is option D: density of the gas and RMS speed of the molecules.