Boyle's law: P1V1 = P2V2. As gases get compressed their volume shrinks.
As gases decompress their volume expands. Taking a 1 cubic foot balloon down
in the ocean would cause it to shrink to 1/2 its size at 33'. Breathing at
depth, ascending, and holding your breath may cause serious lung over-expansion
resulting in arterial gas embolism, etc.
Henry's law: A gas over a liquid will flow into the liquid until the pressure
is equal. If you covered a lake with neon, the atoms of that gas would pass
though the surface of the water until the neon in the water had the same
pressure as what is left in the air.
Charles's law - When you heat a gas in a container that is closed the pressure
of the gas will rise. Likewise, if you cool the gas the pressure will drop.
Likewise, if you decrease the pressure on a gas it will cool. If you take
your scuba tank to have it filled and they fill it fast, the temperature
will rise. As time goes by the air and tank will cool down. When that happens
the pressure in the tank will drop. So, pressure, temperature, and
changing gas volume are all related.
Dalton's law: When you have a mixture of gases, each gas contributes to the
total pressure. If you have a container of air that is at 2 atmospheres,
21% of the 2 atmospheres (0.42 atm.) is due to the oxygen, and 78% (1.56
atm) is due to the nitrogen. Both gases exert their own pressure and the
two are combined to find the total pressure.
I found an article in the January 2005 scuba magazine
Dive Training entitled
Phiddling With Physics: Understanding the Gas
Laws. It was so well written by Alex Brylske, the Senior Editor
of the magazine, that I ask for and received his permission to include it
here:
Phiddling With Physics: Understanding the Gas
Laws
By Alex Brylske
While most scuba instructors are careful to avoid using
the term directly, a good many of the concepts we must understand to dive
safely involve the dreaded p-word, physics. We almost never utter this term
because, quite frankly, it scare the daylights out of most folks. After all,
physics is that obtuse and impossibly complex subject that only people like
Albert Einstein or Steven Hawking can comprehend. This fact was perhaps
reinforced by the F you received when, by some misguided advice of a guidance
counselor, you took the class in high school.
Of course, as often happens with science, misconceptions
abound, and reality is sometimes a far cry from perception. So is the case
with physics. Contrary to what you might believe, it was not invented to
torture under-achieving high school students, or confuse common sense. At
its root, physics is really the science explaining the most familiar experiences
in daily life. The dictionary defines it as "the scientific study of matter,
energy, force, motion, and the way they relate to each other." In a way,
physics is the science of everything. But understanding what you need to
know about the physics of diving is as easy as pie-or rather, pi.
Does it Matter?
The raw material of physics is matter, which is the ultimate
catch-all word for anything with substance-virtually everything. Unless you
snoozed through junior high school science, you probably already know that
all matter is made up of elements that can be combined into compounds. At
the tiniest level of any practical consequence, matter consists of molecules.
Furthermore, matter exists in three states-solid, liquid
and gas. At relatively low temperatures, molecules assume the rigid state
that we term solid. Although the molecules comprising a solid vibrate, they
remain in fixed positions. As temperature increases, the fixed structure
of the molecules disappears, and the matter "melts" into a liquid state.
In a liquid, the molecules vibrate faster than in a solid, so they aren't
held together rigidly. A good way to conceptualize a liquid state is to think
of the rubber ball pits common at children's playgrounds like, for example,
at a MacDonald's Playland. While the balls are close together, they easily
slip and slide past each other. So, a child playing in a ball pit is somewhat
like someone swimming in the world's most viscous fluid. At still higher
temperatures the molecules move further apart, like the ping-pong balls you
see in pneumatic lottery machines. Finally, they break free from the surface
of the liquid, and become a gas.
For this discussion, we'll consider all solids and liquids
incompressible. But gases, because of the extreme relative distance between
their molecules, are highly compressible. As divers, we deal in an environment
with rapidly changing pressure, so this is of enormous consequence to us.
Air is a gas comprised mainly of nitrogen, oxygen, argon
and carbon dioxide. So, although it's invisible, air and all other gases
have substance; they are matter. Although this idea had been around since
the days of the ancient Greeks, it was left to the famous seventeenth century
astronomer Galileo to prove it. (Frankly, when you think about it, the fact
that air has substance is really a matter of common sense; it's evident every
time winds blow.) Later, Galileo's secretary, a mathematician named Evangelista
Torricelli, showed that the atmosphere exerted enough pressure to hold up
30 inches/76 centimeters of mercury within a vacuum tube. A French mathematician
named Blaise Pascal proved that the weight of the atmosphere was equal to
the pressure exerted by 33 feet/10 meters of sea water.
Boyling the Air
The granddaddy of gas experts was a renowned English
scientist named Robert Boyle (after he got famous, it was Sir Robert Boyle).
Building on Toricelli's work, he discovered that when they are exposed to
either increased or decreased pressure, gases' behavior are highly predictable.
He expressed his prediction mathematically in what has come to be known as
Boyle's Law. Without all the algebra and scientific mumbo-jumbo, Boyle's
Law essentially says that if you increase the pressure on a gas-filled
object-like a balloon-the volume gets smaller. Squeeze a balloon and it gets
smaller. Obviously, this stuff isn't rocket science. Of course, Boyle's Law
acts in the exact opposite way when the pressure is reduced-like when a diver
ascends. According to Boyle's Law, if we release a sealed balloon at depth,
it will expand as it ascends; and if it exceeds its maxim volume, it will
burst. So, too, when reducing the pressure on ascent, our lung volume increases.
If we do nothing about it-like exhale-we risk lung injury due to overexpansion.
Ironically, while Boyle discovered his "Law," he could
never explain what was actually happening. That took another scientist, the
Italian Daniel Bernoulli, who explained that as gas, molecules collide with
the container walls (remember the ping-pong balls). The more they're agitated,
the more collisions occur and the greater the force. Bernoulli concluded
that when the density of a gas increases, the number of collisions will also
increase. This is like adding more ping-pong balls to the container. The
increase in the number and force of collisions is what causes the pressure
increase.
Every diver is introduced to Boyle's Law in their entry-level
training. But just in case you're a little rusty, recall that for every 33
feet/10 meters of descent, sea water pressure increases by 15 psi or 1 atmosphere
or atm. (I know, it's really 14.7, but decimals only complicate things here,
and 15 is close enough for government work.) This means that at 99 feet/30
meters, the pressure is four times the surface pressure; three contributed
by the water and one by the atmosphere. (99/33 = 3 + the surface pressure
of 1 atm. = 4 atm.).
Similarly, a volume of gas in a flexible container like
a balloon will also decrease predictably according to the depth (pressure).
For example, at 33 feet/10 meters (2 atm.) the balloon will decrease to 1/2
its surface volume. At 66 feet/20 meters (3 atm.) it decreases to 1/3, at
99 feet/30 meters (4 atm.) to 1/4 and so on. The reverse holds true on ascent.
The volume of a balloon partly inflated at 99 feet/30 meters (4 atm.) will
increase four-fold if it's taken to the surface.
This constant relationship gives divers a neat little
way to estimate how gas volumes change as they ascend or descend. Let's try
an example. Assume that a balloon containing 20 liters of air at the surface
is taken to 100 feet or 4 atm. (yes, 4 atm. is actually 99 feet, but one
foot isn't worth arguing over.) By expressing the problem as a fraction where
the original surface quantity (20) is the top number-the numerator, for the
less mathematically-challenged-and the pressure at 100 feet (4) is the bottom
number or denominator, we have 20/4 or 5 liters (once the fraction is reduced).
You can solve even more complex problems with this fractional
relationship. Let's assume a balloon contains 5 liters at a depth of 66 feet/20
meters. What will its volume be if it's taken to 33 feet/10 meters? First,
let's see what happens to the balloon if it's taken to the surface. As 66
feet/20 meters is 3 atm., the balloon will expand three-fold when it reaches
the surface and contain 15 liters (3 x 5 = 15). Now, simply use the same
fractional relation from the previous problem. The surface volume (15) over
the pressure (2), or 15/2. Reduce the fraction to 7.5. Thus, the balloon
would change from a volume of 5 liters at 66 feet/20 meters to 7.5 liters
at 33 feet/10 meters.
The only drawback to this quick and dirty method of
calculation is that it only works if you use atmospheres as increments. For
more precise results, or for problems expressed in terms other than atmospheres,
you'll have to use the dreaded mathematics of algebra, and famous equation
P1V1=P2V2. The point is that the implications of Boyle's Law are easily
determined using nothing more than some logic, common sense and simple
arithmetic. You didn't even have to use a calculator!
The Plot Thickens
While understanding the relationship of pressure and
volume is both vital and obvious to all divers-it explains the most important
rule of scuba diving-fewer understand why density is just as important. Like
pressure and volume, though, understanding density is also a matter of common
sense.
To begin, let's squeeze the balloon again. As you saw
before, this reduces its internal volume. So, if the volume is reduced, the
molecules within the balloon have to come closer together. (Think of a conductor
pushing a crowd of people aboard a subway car.) In other words, the air gets
"thicker," but the more appropriate term is denser. There is one important
difference between pressure/volume and pressure/density relationships, however.
Note that the former relationship is inversely proportional-if one factor
goes up, the other goes down. In the latter, the relationship is directly
proportional-if one factor goes up, so does the other.
Luckily, the change in the density of a gas is as predictable
as the change in its volume. If, for example, you take a flexible container
to 2 atm. ( 33 feet/10 meters) the volume will decrease by 1/2 but the density
will double. In turn, at 3 atm the volume will be one-third and the density
will triple; at 4 atm. the volume is now one-fourth and the density quadrupled
and so on. This relationship is important because it explains why a diver
consumes his air more rapidly the deeper he goes. Here's why.
In free diving (breath hold), as a diver descends, his
lungs decrease in size according to Boyle's Law. But this isn't the case
when using scuba because a diver fills his lungs completely with every breath.
To fill the lungs, the density of the air inhaled must increase to equal
the ambient (surrounding) pressure. In fact, as we saw earlier, the air in
a breath taken at 33 feet/10 meters will be twice as dense as at the surface.
Likewise, to get a lung full of air at twice the density of the surface,
twice the number of molecules must be drawn from the tank. So, as the diver
is drawing twice the number of molecules from the tank at 33 feet/10 meters,
his air supply will last only half as long as it would at the surface. Similarly,
if all other conditions are equal, the air supply will last only one-third
as long at 3 atm (66 feet/20 meters), one-fourth as long at 4 atm. (99 feet/30
meters), and so on.
Knowing this relationship gives you an easy way to estimate
how long your air supply will last. But be forewarned, this is only a rough
estimate. Your actual air consumption rate varies drastically due to factors
such as cold, heavy exertion and stress. Additionally, the estimate works
only if you plan to remain at a constant depth throughout the dive-something
we divers rarely do.
You're Getting Warmer
Sir Robert Boyle's work dealt solely with the effects
of pressure and volume. He did not consider the effect of a third important
factor-temperature. The influence of temperature on gas behavior was first
explored by a French scientist named Jacques Charles and his colleague, Joseph
Gay-Lussac.
Through experimentation, Charles and Gay-Lussac found
that if they kept the pressure of a gas constant in a container, the volume
of the gas would increase as the temperature increased. Conversely, the volume
would decrease when the temperature decreased and the pressure remained constant.
This is called Charles' Law, and it explains, for example, why, if you leave
an inflated balloon in a hot car all day it will expand.
One way Charles' Law relates to diving is in how temperature
affects the pressure in a scuba tank. As a general rule, for every change
in temperature of one degree Fahrenheit, the pressure in a scuba tank changes
about 5 psi. For every change in temperature of one degree Celsius, the pressure
in a scuba tank changes about 9 psi. To do more precise calculations requires
a little simple algebra; but at least you now understand why your tank's
burst disk let go that time you forgot and left it in your trunk on a hot
summer day.
Years later a researcher named Julius Mayer explained
the phenomenon Charles and Gay-Lussac described. He suggested that heat is
simply a result of molecular motion. Therefore, increasing the temperature
was merely increasing the motion of the molecules. As the molecules increased
in motion, they increased in their frequency of collision. This is measured
as an increase in pressure. In 1843, the scientist James P. Joule proved
Mayer's theory experimentally. Incidentally, if you're not terribly afraid
of a little math, both Boyle's and Charles' Laws can be integrated into what's
called the General Gas Law. This lets us predict gas behavior regardless
if the factors that vary are volume, pressure or temperature.
Mixed Gas
So far, nothing we've discussed considers what happens
when different gases are mixed together. While this may seem a trivial matter,
it's anything but. In fact, not knowing how gases behave in a mixture can
get a diver killed. The first person to explore this phenomenon was an English
scientist, John Dalton. (In addition to his work with gases, Dalton is famous
for his work describing matter as being comprised of atoms).
Dalton found that even though a gas mixture is made up
of several different constituents, each gas will continue to demonstrate
its own individual behavior, as though the other gases didn't exist. Again,
more common sense; if a gas mixture is made up of 80 percent nitrogen and
20 percent oxygen, then it stands to reason that 80 percent of the pressure
is exerted by the nitrogen and 20 percent by the oxygen. However, this tidbit
of common sense is so important that it's called Dalton's Law.
Furthermore, Dalton termed these individual pressures
within a mixture partial pressures; and he found that each partial pressure
is proportional to the number of molecules of that gas within the mixture.
Let's see how this concept applies to us as divers.
Let's return again to our gas mixture of 20 percent oxygen
and 80 percent nitrogen, and we'll assume it's at a pressure of 15 psi. This
is similar to our own air, but ignores the trace gases, and working in round
numbers makes the concept easier to understand. According to Dalton's Law,
oxygen exerts 20 percent of the total pressure of the gas, while nitrogen
exerts 80 percent. Another way of stating this is that of the 15 psi total
pressure, the partial pressure of the oxygen exerts 3 psi (20 percent) while
nitrogen partial pressure exerts the other 12 psi (80 percent).
Now let's double the total pressure to 30 psi and see
what happens. (We'll assume the temperature remains constant at all times.)
Each gas component continues to exert its partial pressure in proportion
to the 80/20 mixture. Of the total 30 psi, nitrogen exerts 80 percent or
24 psi, and oxygen exerts 20 percent or 6 psi.
If the ambient pressure increases, the pressure inside
the container (such as our lungs) also must increase for the container to
maintain its original volume. This means more gas must be put in the container
to increase the internal pressure. As we saw before, this is exactly what
happens when a diver breathes from his regulator at depth; more gas molecules
go into his lungs to maintain a constant lung volume.
Note that while the percentages of the gases that make
up the mixture never change, the number of gas molecules increases to exert
more pressure. This means more molecules of each gas reach the diver's lungs.
For example, let's assume a lung volume at the surface contains 100 molecules
of air. (Of course the real number would be vastly more than this, but a
small, round number makes it easier to understand.) If we continue to assume
an 80/20 nitrogen-oxygen mixture, then of the total 100 molecules, 80 will
be nitrogen and 20 oxygen.
Now assume the diver descends to 132 feet or 5 atm. At
that depth the ambient pressure is five times what it was at the surface.
So, to maintain a normal lung volume, the diver takes in 500 molecules with
each breath. This is five times the number he breathed at the surface. As
this is still an 80/20 gas mixture, nitrogen accounts for 400 molecules or
4 atm. of pressure, while the oxygen component is responsible for 100 molecules
or 1 atm. Notice that breathing this air mixture at 132 feet is physiologically
equivalent to breathing pure oxygen at the surface-100 molecules at one
atmosphere.
We can demonstrate the insidious nature of increasing
partial pressures in yet another way. Suppose that while filling a scuba
tank a one percent quantity of carbon monoxide enters the mixture. Using
the previous example of 100 molecules to equal a full lung, carbon monoxide
would now account for one of the 100 molecules inhaled with each breath while
at the surface. But, if the diver descends to 99 feet (4 atm), his lungs
now require 400 molecules to fill-four times the surface quantity. Of those
400 molecules drawn from the tank with each breath, carbon monoxide will
now account for four molecules. The problem is, breathing these four molecules
of carbon monoxide at 99 feet has the same physiologic effect as breathing
a gas mixture of four percent carbon monoxide at the surface (which is toxic).
Thus, we see why an air supply that might contain tolerable
levels of contaminants at the surface can quickly become toxic at depth even
though the gas inside the tank never changes. Once the tank is full, the
proportion of gases in the mixture remains unchanged. The problem results
purely from breathing the mixture under higher pressure; and it's all a result
of the good Doctor Dalton's Law.
Bubbles 101
As a science educator, one of the more difficult concept
for my students is understanding that gases can dissolve into liquids. The
reason is that the concept seems to belie reality. For example, to the naked
eye a liquid doesn't appear to have any "space" in it to allow gas to enter.
However, we all know better; gases can dissolve into liquids. We're reminded
of this every time we pour a can of soda into a glass of ice. The profuse
formation of bubbles is merely carbon dioxide being released from the liquid.
The gas, although not visible in its dissolved form, remains in solution
until something acts on it to make it come out. The other important concept,
beside the fact that gas can be held inside a liquid, is that the gas also
continues to exert pressure while in solution. This internal pressure is
called gas tension.
Exactly how much gas a liquid will absorb, and what factors
affect this absorption, was first studied by a colleague of Dalton's named
William Henry. His experiments proved that the amount of gas that dissolves
into a liquid at a given temperature depends on the partial pressure of the
gas. Yep, you guessed it. This concept is called Henry's Law, and it's yet
another phenomenon that we've all experienced. Why, for example, does a freshly
tapped keg of beer taste better than the dregs at the end of the keg?
Simple-because of Henry's Law. More gas-in this case, carbon dioxide-is dissolved
in the liquid when it's first tapped. But over time, as the carbon dioxide
dissipates, the contents "go flat." The decline in taste results from the
reduced gas tension in the liquid.
Henry's Law further tells us that both pressure and
temperature affect how gas dissolves into liquids. Let's see how this might
happen. Imagine you have a beaker of water with absolutely no gas dissolved
in it. The beaker is also inside a chamber where a perfect vacuum exists.
This means that absolutely no gas is in contact with the water. (These conditions
are impossible to achieve except perhaps in outer space, but it makes the
concept easier to understand.) If air enters the chamber and comes in contact
with the water, air molecules begin dissolving into the water. The gas in
the water then exerts a pressure, or gas tension. In addition, the gas tension
will obey Dalton's Law and each component gas continues exerting its own
partial pressure.
Gas will attempt to dissolve into liquid until the gas
tension equalizes with the air pressure in contact with the liquid. But this
takes time. The difference between the air pressure in contact with the liquid
and the gas tension within the liquid is called a pressure gradient. If the
pressure gradient is high, gas will be absorbed into the liquid quickly.
But, as the gas molecules continue to dissolve into the water, the gradient
begins to decrease. Molecules dissolve into the water more slowly.
Over time the gas tension in the water equals the air
pressure in contact with the liquid. Although molecules will continue to
pass between the liquid/air interface, no net exchange of gas occurs. The
water is now said to be saturated.
Let's now pressurize the vacuum chamber. This increases
the pressure of the gas in contact with the water. This causes even more
gas to dissolve into the water. Over time, gas will continue to enter the
water until the gas tension in the liquid and the air pressure on the liquid
are equal (saturation). As Henry's Law predicted, the more pressure the gas
exerts on the water, the more gas dissolves into the water.
As you might expect, if we release the pressure in the
chamber the phenomenon is reversed. With less pressure on the water, the
gas dissolved in it has a greater gas tension than the air in contact with
the water. Now the water contains more gas than it can keep in solution at
that pressure.
Gas transfers out of the liquid until the gas tension
is equal to the air pressure. If air pressure is reduced very slowly, if
it isn't shaken, or if no foreign particles are present in the water, the
gas transfer is undetectable-no gas bubbles form. But if the air pressure
decreases too quickly, or the water is vigorously shaken, or if foreign particles
are added to the water, the gas begins to escape more rapidly. So quickly
that-like a shaken bottle of soda-the gas molecules will form visible bubbles.
In addition to pressure (Boyle's Law), temperature (Charles'
Law) also affects gas absorption into liquids. Heat makes the molecules of
a liquid vibrate more activity. This rapid movement leaves less space in
the liquid for gas molecules to occupy. Now, fewer gas molecules can dissolve
into or remain in the liquid. We see this take place anytime we boil water.
As the water begins to heat, small air bubbles form and collect at the bottom
of the container. They're caused by the speeded-up molecules pushing dissolved
gas out of the water. It makes sense, then, that cooler liquids can hold
more dissolved gas than warmer liquids. A cooler liquid contains slower
molecules, allowing room for more gas molecules to occupy.
If you haven't already figured out why this phenomenon
is so important, it's because gas dissolves into our blood and other tissues
just as it dissolved into the beaker of water. But absorption isn't as big
a concern as elimination; the real problem begins when pressure is reduced
and the gas has to come out. Under certain circumstances, this could lead
to significant bubble formation and decompression sickness. There are, however,
some important differences between body tissues and a beaker of water, which
makes understanding the mechanism of decompression sickness a bit more
complicated than the oft-used "shaken bottle of soda" analogy. Still, whether
it's carbon dioxide dissolving into soda water or nitrogen into the bloodstream,
the physics is all the same.
