9.2

The Ideal Gas Law

An ideal gas obeys PV = nRT, linking pressure, volume, temperature, and quantity of gas through simplifying atomic assumptions.

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Context

What this topic is and why it exists

Imagine a room full of tiny, perfectly bouncy ping-pong balls flying in every direction, never sticking together, never slowing down, and so small compared to the room that they're practically invisible dots.
That's an ideal gas.
It's not a real thing you'll find in nature — it's a beautifully simple mental model that lets us predict how gases behave without drowning in complexity.
The rules are straightforward: the gas atoms move randomly, they take up almost no space themselves, they bounce off each other and the walls without losing any energy, and they completely ignore each other except during those split-second collisions.
From these simple assumptions flows one elegant equation: PV = nRT.
Pressure times volume equals the amount of gas times a constant times the temperature.
That's it.
This single relationship lets you predict what happens when you squeeze a gas into a smaller space, heat it up, or let some escape.
And here's something beautiful: if you graph pressure against temperature and follow the line downward, it points to a temperature where pressure would hit zero — absolute zero, the coldest anything could theoretically get.
No one has ever reached it, but the math of bouncing ping-pong balls predicted it had to exist.
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