The air in a classroom has a density of 1.20 kg/m³ at a pressure of 1.02 × 10⁵ Pa…
Contributed by StemPy LabTry 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 at a pressure of 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 in each hit, and hits it times each second. For a gas:
where 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.
Plan. The pressure formula links , and . We want the speed.
Step 1. , so .
Step 2. m/s.
Answer: about m/s, a little faster than sound in air.
Watch out. Pa divided by kg/m³ is m²/s², so the square root is in m/s. Check the units this way when you are unsure.
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