The way gases behave changes a lot depending on pressure, temperature, and volume. This is explained by something called gas laws.

1. Pressure and Volume (Boyle's Law): When the temperature stays the same, the volume of a gas and its pressure have an opposite relationship. This means if one goes up, the other goes down.

   Here's how it looks mathematically: $P_1 V_1 = P_2 V_2$

   For example, if the pressure of a gas goes from 1 atm to 2 atm, the volume will shrink to half its size, as long as the temperature does not change.

2. Volume and Temperature (Charles's Law): This law tells us that if the pressure stays the same, the volume of a gas goes up when its absolute temperature goes up.

   You can see this in this equation: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

   For example, if you heat a gas from 273 K to 546 K while keeping the pressure steady, its volume will double.

3. Pressure and Temperature (Gay-Lussac's Law): This law shows that when the volume of a gas stays the same, the pressure directly changes with the temperature.

   This is how it's expressed: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

   So, if you raise the temperature from 300 K to 600 K, the pressure of that gas will double.

By understanding these gas laws, we can better predict how gases will act in different situations. This knowledge is really important for many scientific uses.