# The volume of gas when the temperature

The depths of the ocean exists in a much different
environment than the one the majority of people are familiar with. Yet, more
than 3 million people brave the unknown with specialised equipment keeping them
alive (“How Many People Scuba Dive? It’s Not an Easy Answer!”). Scuba Diving
has been an extreme sport that attracts more and more people each year, due to
its safety record and the allure of entering an exotic and foreign environment
(Ange). However, this sport is not without its challenges, as the underwater world
contains different physical properties different than on land. Light refracts
differently, apparent weightlessness becomes both a blessing and a curse, and a
humans body temperature drains much faster than it seems. Therefore, each and
every diver is taught to behave in certain ways and to bring certain equipment
to counteract the different properties that exist in the deep. Diver’s must
never hold their breath, wear appropriate diving suits, and wear diving goggles
due to the physics that underlies this underwater realm.

One of the first things divers are taught is the most
important rule of all: Never hold your breath. This might seem counterintuitive
at first since logically divers would want to conserve as much air as possible.
However, there is a simple physical explanation that is fatal if not fully
appreciated. Air is a gas that everyone requires and is stored in a diver’s gas
tank. However, once released air will be subjected by several conditions. As
air is a gas, it can be reasonably approximated as an Ideal Gas, which can,
therefore, be described using the Ideal Gas Law,

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where the product of the pressure P and volume V is equal to
the product of the absolute temperature T, the amount of gas in moles n, and
the gas constant R (Young 592). Assuming that the diver holds his breath and
that the temperature underwater is constant, then the relationship simplifies to
Boyle’s Law,

which states that pressure is inversely proportional to the
volume of gas when the temperature is constant (Young 596). The pressure
underwater can be approximated to an increase of 1 atmosphere of pressure for
every increase of 10 metres (NOAA 1).

Figure 1. Shows the
size of a diver’s lungs change as a function of depth

Holding a breath underwater and descending is physically
acceptable yet not recommended, as the volume of the gas in the air decreases
as the pressure dive, however it is extremely discouraged. Meanwhile, holding
their breath and ascending is dangerous.

As an example, given that the lung has an approximate volume
of 6 litres of air, if a diver holding his breath at full capacity from a depth
of 20 meters to 10 meters, the gas in his lungs would expand following Boyle’s
Law (Elert). This means that the gas volume can be calculated as

The volume would, therefore, be 9 litres, 3 litres more than
the total lung capacity of an average human which would mean that the lung will
burst. Holding breath shuts off the lungs from releasing the continuously
expanding air as the diver ascends with disastrous consequences, which is why
divers are taught to continuously breathe to allow the lung to regulate and
adapt to the volume of air it holds under pressure.

Divers are rarely seen wearing just swimming clothes, and
this is because they tend to get chilled quickly. Temperature naturally behaves
differently in water than in air due to the differing properties they have. In
fact, the specific heat of water is 4.184 Jg-1K-1 , and a
thermal conductivity of 0.6 Wm-1K-1, compared to air’s 1 Jg-1K-1
and 0.024 Wm-1K-1 (Perlman, “Thermal Conductivity”,
“Specific Heat of Dry Air”). Given that the water temperature in diving is
around 0-30°C, being less than the temperature of the human body, heat will
flow from the diver to the water (“Sea Temperatures”).  Combined, not only does this mean that divers
would lose thermal energy to the surroundings, but they would lose this energy
at a much faster rate.

Therefore, divers have created several types of equipment
that conserve warmth to keep the diver comfortably heated. The two most
important types of equipment are wetsuits and drysuits, both of which trap heat
albeit in different ways. Wetsuits are made of neoprene, a rubber which
contains nitrogen bubbles. The nitrogen bubbles perform a variety of tasks; the
bubbles have low conductivity and therefore retains their heat from before the
dive longer, and it also prevents convection from occurring between the trapped
water inside the wetsuit with the colder water outside (“How do wetsuits
work?”). Furthermore, wetsuits are typically lined with a small layer of
reflecting metals such as titanium in order to reflect the trapped heat back
into the body. Wetsuits aren’t completely waterproof, allowing water to flood
the insides with the seams on the arms and legs partially trapping them. This
allows the trapped water to be heated by the body temperature and traps the
heat inside the wetsuit, which allows the diver to retain their body heat
longer.

Figure 2. An example of a wetsuit

Drysuits, on the other hand, are completely waterproof and
keep the water out of the suit. This leaves a layer of air surrounding the
diver, keeping the diver insulated. As air is a much better insulator than
either water or neoprene, a drysuit is capable of keeping the diver warm even
if the outside temperature is much colder.

Therefore, drysuits are much better suited for colder dives
of below 10°C (“Stay Warm”). However, other than that they function identically
to wetsuits, in that they both trap heat and prevent it from escaping to the
surrounding ocean, helping the diver conserve their warmth for a longer period
of time.

One iconic equipment that divers are known to use are diving
goggles, which serves multiple purposes, yet the most important of which is
allowing divers to see underwater. It is well known that everything underwater is
blurry when viewed from underwater without goggles. This is mainly due to how
water alters the way light travels through this medium and how our eyes
perceive objects. Our eyes have lenses that are normally suited to focus light
rays that travel in air, with specific components that focus the light
correctly.

Fig 3. Diagram of the important parts of an eye (“Image
Formation and Detection.”)

As seen in Fig. 3, the cornea is the first interface that
light passes through. The cornea has a refractive index of 1.38, which is
drastically different than air’s refractive index of approximately 1 (“Image Formation
and Detection”). The rest of the eye have slightly different refractive indexes
compared to the cornea, however as the rest only slightly refracts the light,
their effects can be considered negligible and it can be assumed that the
entire eye has a refractive index of 1.38.

The eye has the ability to adjust its focal length such that
most images are focused on the back of the eye, thereby allowing it to keep the
image distance constant (“Image Formation and Detection”). The relationship
between the focal distance of the eye f, the object distance from the lenses s,
and the image distance s is

also known as the object-image relationship (Young 1132). As
an example, if an object is 1 metre away and the image distance is fixed at 1.8
cm — the distance between the lens and the retina (“Image Formation and
Detection”)—, then the focus at this configuration is

Since the eye is a lens, the eye can be
described using the Lensmaker equation

where f is the focal distance of the eye,
nl is the refractive index of the lens, nm is the
refractive index of the medium, and 1/r1 – 1/r2 is a constant, with r1 and r2
being the radius of the first and second lens respectively (Young 1134).

In the example above, since the radius of
the eye is constant, and combining the Lensmaker equation and the object-image relationship,
the radius constant can be calculated as

This is the basic configuration of the
eye when it views objects with air as its medium.  However, when our eyes are underwater, the
light will no longer be travelling through an air-eye interface, rather it will
be through the water-eye interface. Water’s refractive index is 1.33, which is
similar to the eye’s refractive index (“RefractiveIndex.INFO.”). Therefore,

This clearly shows that the image forms
behind the eye and not directly on it, which is why everything is out of focus
when viewed without a protective device such as goggles.

Fig. 4 a) shows the light focusing behind
the eye from a water-eye interface b) shows how an air pocket corrects for this
property (Heath 9)

Goggles provide a pocket of air directly
in front the eye, allowing light to be refracted through the air-eye interface
instead of the water-eye interface. Aside from simply keeping water out of our
eyes, goggles play an important role in allowing divers to observe objects
clearly underwater.

These physics properties are only the tip
of the iceberg when it comes to diving, yet these are the ones that most
directly affect divers. Divers should never hold their breath, wear the
appropriate attire, and bring their diving masks for them to dive safely and
comfortably. These are all the consequences of the different physics that
occurs underwater, yet all of them have been overcome safely due to the diver’s
understanding of their environment and adequate preparation. Even now, people
are developing better equipment for divers to stay in the water more
comfortable, deeper, longer, and all the more comfortable.