Question

How does Charles' law relate to scuba diving?

Answer 1

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.

`V ∝ T`

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.

`P ∝ T` or `P_1/T_1 = P_2/T_2`

A scuba tank is full when the gauge shows the "full" pressure at a temperature of 20 °C.

EXAMPLE

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?

Solution

`P_1/T_1 = P_2/T_2`

`P_2 = P_1 × T_2/T_1 = "200 bar" × (283.15 cancel("K"))/(313.15 cancel("K")) = "181 bar"`

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.