An ideal gas is contained in a cubical box of side length $a$ - AQA - A-Level Physics - Question 10 - 2020 - Paper 2

The force exerted by the gas molecules on the walls can be derived from the change in momentum of the molecules during collisions. For an ideal gas, the total force on one wall can be given by:

$F = \frac{Nm v_{rms}}{t}$ where $v_{rms}$ is the root-mean-square speed of the gas molecules.

The root-mean-square speed for an ideal gas is given by:

$v_{rms} = \sqrt{\frac{3kT}{m}}$ where $k$ is the Boltzmann constant and $T$ is the temperature.

The area ($A$) of one side of the cubical box is:

$A = a^2$

Substituting the expression of force and area into the formula for pressure:

$P = \frac{F}{A} = \frac{\frac{Nm v_{rms}}{t}}{a^2}$

Thus, after substituting $v_{rms}$, we can find the final expression for pressure exerted by the gas on the walls of the box.

After evaluating the expressions, the correct answer for the pressure exerted by the gas on the walls of the box corresponds to option D: ( \frac{mN}{3a^2} \times \text{cm}^{-2} ).