At
constant temperature, the absolute pressure and the volume of a gas are
inversely proportional. Thus, as
the pressure is increased the volume of a gas is reduced. This law is often presented as:
P1 x V1 = P2 x V2
Legend: P1
= the initial pressure
V1 = the initial volume
P2 = the final pressure
V2 = the final volume
The initial pressure times the initial volume of a
gas is equal to the final pressure times the final volume of the gas.
For example, if one cubic foot of gas at the surface
is taken to a depth of 33 fsw, what would the final volume of the gas be>
We know that the initial absolute pressure is P1 = 1
atmospheres absolute (ATA). The
final absolute pressure is P2 = 2 ATA.
The initial volume is V1 = 1 cubic feet.
Therefore to determine the final volume we would use Boyle’s Law as
follows:
P1 x V1
1 ATA x 1 cubic foot
V2 =
---------
=
--------------------------
= 0.5 cubic feet
P2
2
ATA
Another example of direct relevance to cave diving is
the rate of gas consumption. A
resting diver on the surface breathes approximately 0.5-1.0 cubic feet of gas
per minute while a lightly working diver breathes 1.0-3.0 cubic feet per minute.
There is a large variation from diver to diver and each diver should
determine his own gas consumption. The
two main factors that determines gas consumption are experience (degree of
relaxation, efficiency moving in the water) and fitness level.
Other factors such as age, body size, etc. are less important.
If a diver’s gas consumption rate was 1 cubic feet
per minute at the surface, how long would it take the diver to breathe 1/3 of
the gas in a set of double 104 cubic feet tanks filled to 2640 psi?
At 2640 psi, each tank will contain 104 cubic feet of gas.
Therefore, the total quantity of gas available is 2 x 104 cubic feet =
208 cubic feet, and 1/3 of that is 208 / 3 = 69 cubic feet.
It takes the diver one minute to breathe one cubic foot and, therefore,
the diver will breathe 1/3 of the gas in a set of double 104’s in
1 minute
69 cubic feet x
------------ =
69 minutes
1
cubic foot
If the diver maintained the same rate of gas
consumption at 130 feet, how long would it take to breathe the same quantity of
gas? The solution can be calculated
by determining the surface-equivalent volume of 1 cubic foot of gas at 130 feet
as follows. The volume at depth is
V1 = 1 cubic foot. The
absolute pressure at depth is
1 ATA
x 130 fsw
P1 = -----------------------
+ 1 ATA
= 4.94 ATA
33 fsw
The
surface pressure is P2 = 1 ATA.
Therefore, the equivalent surface volume is:
P1 x V1
4.94 ATA x
1 cubic foot
V2 =
---------- =
--------------------------------
= 4.94 cubic feet
P2
1 ATA
Therefore,
our diver is using 4.94 cubic feet of gas per minute and has 208 / 3 = 69 cubic
feet of gas to use. The diver will
breathe this volume of gas in 69 / 4.94 = 14 minutes. If, however, the diver is swimming moderately hard and gas
consumption increases to 2 cubic feet per minute equivalent surface volume, 69
cubic feet of gas will last only 7 minutes!
