Charles’ law is closely related to Boyle’s Law and states that at constant pressure, the volume of a gas is directly proportional to the change in absolute temperature. This means that as the temperature is increased the volume of a gas increases. This law is often presented as:
V1 V2
--- = ---
T1 T2
Where V1 = the initial volume
T1 = the initial temperature in absolute
V2 = the final volume
T2 = the final temperature in absolute
It is vital to remember to convert all temperature measurements to absolute. On the centigrade scale, absolute zero is minus 273 degrees C and therefore 273 degrees C must be added to all temperature measurements. On the Fahrenheit scale, absolute zero is minus 465 degrees F and therefore 465 degrees F must be added to all temperature measurements.
When
Boyle’s Law and Charles’ Law are combined, the General Gas Law is produced. It can be represented as:
P1 x V1 P2 x V2
---------- = ----------
T1 T2
Where P1 = the initial pressure
V1 = the initial volume
T1 = the initial temperature in absolute
P2 = the final pressure
V2 = the final volume
T2 = the final temperature in absolute
With this law any value can be determined as long as
the other values are known or unchanged. For
example, if an 80-cubic-foot tank was filled to 3000 psi in a water bath at 70oF,
the tank was then left in a car in the sun and the temperature of the tank
increased to 200oF, what would the final pressure in the tank be? In this example the initial volume and the final volume are the same, the
initial pressure is P1 = 3000 psi, the initial temperature is T1
= 70 oF + 465oF = 535o absolute, and the final
temperature is T2 = 200oF + 465o F = 665oF
absolute. Therefore the solution
can be determined by:
P1 x T2 3000 psi x 665o absolute
P2 = -------- = ------------------------------- = 3729 psi!
T1 535o
absolute
This is not an impossible example as tanks can easily
reach a temperature of 200 oF is they are left in the trunk of a car
in the sun.
If the same tank had been rapidly filled in the sun
and reached a temperature of 200 oF and 3000 psi when filling was
completed, the pressure in the tank at the start of a dive in water at 70 oF
can be easily determined as follows:
P1 x T2 3000
psi x 535o absolute
P2 = -------- = ------------------------------- = 2414 psi!
T1 665o
absolute
Therefore, for optimal diving it is important to fill tanks in a water bath at a temperature near the temperature of the dive. For safety reasons, tanks should not be allowed to heat up significantly between filling and diving. On a hot summer day where it is impossible to prevent the tanks from warming up, consideration should be given to under-filling them slightly.
