The air in a classroom has a density of 1.20 kg/m³ at a pressure of 1.02 × 10⁵ Pa…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The air in a classroom has a density of $1.20\ \text{kg/m}^3$ at a pressure of $1.02 \times 10^5$ Pa. Treat the air as an ideal gas. How fast, on the rms measure, do its molecules move?

Need a reminder? The key ideaShow

A molecule bouncing off a wall gives it the momentum $2mv_x$ in each hit, and hits it $\dfrac{v_x}{2L}$ times each second. For a gas:

\displaystyle p = \tfrac13 nm\bar{v^2} = \tfrac13\rho\bar{v^2} = \tfrac23\,\frac{E}{V}

where $E$ is the total translational kinetic energy.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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