# Thermodynamics 2: The Gas Laws

Last chapter, we talked about a piston that can change the pressure and volume of a gas in a cylinder. It turns out that if the amount of gas does not change and the temperature does not change, then the pressure and volume from state 1 to state 2 are related like so

which is called *Boyle’s Law.* So the product of pressure times volume is constant. In order for this product to remain constant, if pressure increases, then volume has to decrease, and *vice versa.* This means that pressure and volume are *inversely* proportional.

If we had a different situation where mass and pressure were held constant, the temperature and volume are related like so

which is called *Charles’ Law.* So the ratio of volume to temperature is constant. In order for this ratio to remain constant, both volume and temperature must increase or decrease by the same percentage. This means that temperature and volume are *directly* proportional.

Thirdly, if we had a situation where the pressure and temperature were held constant, we find that the volume and amount of gas ( is in moles) are related like so

which is called *Avogadro’s Law.* In order for this ratio to remain constant, the volume and the amount of matter must increase or decrease by the same percentage. This means that volume and amount of matter are *directly* proportional.

We can relate pressure, temperature, volume and amount of gas using the ideal gas law,

where is the number of moles of gas, and the ideal gas constant, 8.314 J/molK. An ideal gas is a theoretical gas that always obeys the ideal gas law. For our purposes, simple gases like hydrogen, nitrogen, and oxygen behave close enough to the ideal gas that this equation works for them.

Say we have a sealed container, so the amount of matter () is constant. We can write

and two different states of the system would be related like so

Next time, we’ll talk about what this is used for.

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