How does Charles' law relate to scuba diving?
Charles' Law does not relate to scuba diving.
Charles' Law is often used to explain why the pressure in a scuba tank goes up when the temperature increases.
But Charles' Law states that the volume of a gas is directly proportional to its temperature.
The volume of a scuba tank is constant. It doesn't change.
The appropriate law to explain this phenomenon is Gay-Lussac's Law or Amonton's Law:
The pressure of a gas is directly proportional to its temperature.
A scuba tank is full when the gauge shows the "full" pressure at a temperature of 20 °C.
Suppose you have a 10 L steel tank holding air at 200 bar and 40 °C. What will be the tank pressure when you go into water at 10 °C?
You have lost about 10 % of your pressure before you ever got into the water.
Ideal situations are about 6 %, and worst case scenarios about 15%.
Nevertheless, few divers claim that this is the reason they run out of air.