Boyle’s Law: Pressure, Volume, and Density
The relationship between pressure, volume, and
density of gases was studied by Sir Robert Boyle in the
seventeenth century. There are four variables that can be
altered in a gas sample–pressure, volume, temperature,
and quantity. Boyle fixed the amount of gas and its temperature
during his investigations. He found that when
he changed the pressure, the volume responded in the
opposite direction.
Boyle’s Law states: “At a constant temperature,
the volume of a gas varies inversely with absolute
pressure, while the density of a gas varies directly with
absolute pressure.” Expressed as a formula, for a given
gas sample:
PV = K
where P is the absolute pressure; V is the volume; and K
is a constant.
As a working formula, we usually use:
P1V1 = P2V2
where the P and V are the absolute pressure and the
volume for any two sets of conditions (the “before” and
the “after”).
A commonplace example Boyle’s Law is the action
of breathing. The diaphragm is a muscle that is located
just below our lungs. When we inhale, we move the
diaphragm downward, and the lungs increase in volume.
This decreases the pressure inside our lungs so that it is
less than the outside pressure. As a result, air flows into
our lungs.
There are three important aspects of Boyle’s law
for divers:
1. Large quantities of gas can be compressed into
cylinders. If the pressure is doubled, twice as much
gas will be in the cylinder.
2. Inhaled air will be denser with an increase in
depth. When diving, the regulator delivers breathing
air at the ambient pressure. Even at recreational
depths, an alert diver can notice that the air feels
“thicker” beyond a certain depth.
Chapter 2-Gases & Gas Mixtures
Gases & Gas Mixtures
19
UNITS OF MEASUREMENT
There are several ways to measure pressure.
In diving, our concern is with multiples of
atmospheric pressure.
One atmosphere is the pressure of the air at
sea level. This is the unit most commonly
used in this book.
In the metric system (International System or
S.I.), a commonly used equivalent is bars.
One atmosphere equals 1.013 bars. This is
not significantly different from an atmosphere
of pressure, and the two are generally used
interchangeably.
Other equivalents can be used:
1 atmosphere = 760 millimeters of mercury
= 29.92 inches of mercury
(the “weather report” measure)
= 101.3 kilopascals (kPa)
= 1.013 bars
= 14.7 lbs/in2 (psi)
= 10 meters of seawater (msw)
= 33 feet of seawater (fsw)
Most of these equivalents are actually close
approximations. In all calculations, 10 msw =
1 bar.
Fresh water is 2.5% lighter than seawater.
You could use 10.25 meters or 34 feet of
fresh water as equivalent to an atmosphere of
pressure. The difference has little physiological
consequence in diving, and in practice,
instrument errors and other approximations
can easily outweigh the 2.5% difference.