## The volume of gas when the temperature

The depths of the ocean exists in a much differentenvironment than the one the majority of people are familiar with. Yet, morethan 3 million people brave the unknown with specialised equipment keeping themalive (“How Many People Scuba Dive? It’s Not an Easy Answer!”). Scuba Divinghas been an extreme sport that attracts more and more people each year, due toits safety record and the allure of entering an exotic and foreign environment(Ange). However, this sport is not without its challenges, as the underwater worldcontains different physical properties different than on land. Light refractsdifferently, apparent weightlessness becomes both a blessing and a curse, and ahumans body temperature drains much faster than it seems. Therefore, each andevery diver is taught to behave in certain ways and to bring certain equipmentto counteract the different properties that exist in the deep.

Diver’s mustnever hold their breath, wear appropriate diving suits, and wear diving gogglesdue to the physics that underlies this underwater realm. One of the first things divers are taught is the mostimportant rule of all: Never hold your breath. This might seem counterintuitiveat 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 fullyappreciated. Air is a gas that everyone requires and is stored in a diver’s gastank. However, once released air will be subjected by several conditions.

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Asair is a gas, it can be reasonably approximated as an Ideal Gas, which can,therefore, be described using the Ideal Gas Law, where the product of the pressure P and volume V is equal tothe product of the absolute temperature T, the amount of gas in moles n, andthe gas constant R (Young 592). Assuming that the diver holds his breath andthat the temperature underwater is constant, then the relationship simplifies toBoyle’s Law,  which states that pressure is inversely proportional to thevolume of gas when the temperature is constant (Young 596). The pressureunderwater can be approximated to an increase of 1 atmosphere of pressure forevery increase of 10 metres (NOAA 1).   Figure 1.

Shows thesize of a diver’s lungs change as a function of depth Holding a breath underwater and descending is physicallyacceptable yet not recommended, as the volume of the gas in the air decreasesas the pressure dive, however it is extremely discouraged. Meanwhile, holdingtheir breath and ascending is dangerous. As an example, given that the lung has an approximate volumeof 6 litres of air, if a diver holding his breath at full capacity from a depthof 20 meters to 10 meters, the gas in his lungs would expand following Boyle’sLaw (Elert). This means that the gas volume can be calculated as  The volume would, therefore, be 9 litres, 3 litres more thanthe total lung capacity of an average human which would mean that the lung willburst. Holding breath shuts off the lungs from releasing the continuouslyexpanding air as the diver ascends with disastrous consequences, which is whydivers are taught to continuously breathe to allow the lung to regulate andadapt to the volume of air it holds under pressure.    Divers are rarely seen wearing just swimming clothes, andthis is because they tend to get chilled quickly. Temperature naturally behavesdifferently in water than in air due to the differing properties they have.

Infact, the specific heat of water is 4.184 Jg-1K-1 , and athermal conductivity of 0.6 Wm-1K-1, compared to air’s 1 Jg-1K-1and 0.024 Wm-1K-1 (Perlman, “Thermal Conductivity”,”Specific Heat of Dry Air”). Given that the water temperature in diving isaround 0-30°C, being less than the temperature of the human body, heat willflow from the diver to the water (“Sea Temperatures”).  Combined, not only does this mean that diverswould lose thermal energy to the surroundings, but they would lose this energyat a much faster rate.

Therefore, divers have created several types of equipmentthat conserve warmth to keep the diver comfortably heated. The two mostimportant types of equipment are wetsuits and drysuits, both of which trap heatalbeit in different ways. Wetsuits are made of neoprene, a rubber whichcontains nitrogen bubbles.

The nitrogen bubbles perform a variety of tasks; thebubbles have low conductivity and therefore retains their heat from before thedive longer, and it also prevents convection from occurring between the trappedwater inside the wetsuit with the colder water outside (“How do wetsuitswork?”). Furthermore, wetsuits are typically lined with a small layer ofreflecting metals such as titanium in order to reflect the trapped heat backinto the body. Wetsuits aren’t completely waterproof, allowing water to floodthe insides with the seams on the arms and legs partially trapping them. Thisallows the trapped water to be heated by the body temperature and traps theheat inside the wetsuit, which allows the diver to retain their body heatlonger. Figure 2. An example of a wetsuit Drysuits, on the other hand, are completely waterproof andkeep the water out of the suit.

This leaves a layer of air surrounding thediver, keeping the diver insulated. As air is a much better insulator thaneither water or neoprene, a drysuit is capable of keeping the diver warm evenif the outside temperature is much colder.  Therefore, drysuits are much better suited for colder divesof below 10°C (“Stay Warm”). However, other than that they function identicallyto wetsuits, in that they both trap heat and prevent it from escaping to thesurrounding ocean, helping the diver conserve their warmth for a longer periodof time.        One iconic equipment that divers are known to use are divinggoggles, which serves multiple purposes, yet the most important of which isallowing divers to see underwater. It is well known that everything underwater isblurry when viewed from underwater without goggles. This is mainly due to howwater alters the way light travels through this medium and how our eyesperceive objects. Our eyes have lenses that are normally suited to focus lightrays that travel in air, with specific components that focus the lightcorrectly.

Fig 3. Diagram of the important parts of an eye (“ImageFormation and Detection.”) As seen in Fig.

3, the cornea is the first interface thatlight passes through. The cornea has a refractive index of 1.38, which isdrastically different than air’s refractive index of approximately 1 (“Image Formationand Detection”). The rest of the eye have slightly different refractive indexescompared to the cornea, however as the rest only slightly refracts the light,their effects can be considered negligible and it can be assumed that theentire eye has a refractive index of 1.38.

The eye has the ability to adjust its focal length such thatmost images are focused on the back of the eye, thereby allowing it to keep theimage distance constant (“Image Formation and Detection”). The relationshipbetween 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). Asan example, if an object is 1 metre away and the image distance is fixed at 1.8cm — the distance between the lens and the retina (“Image Formation andDetection”)—, then the focus at this configuration is   Since the eye is a lens, the eye can bedescribed using the Lensmaker equation   where f is the focal distance of the eye,nl is the refractive index of the lens, nm is therefractive index of the medium, and 1/r1 – 1/r2 is a constant, with r1 and r2being the radius of the first and second lens respectively (Young 1134).  In the example above, since the radius ofthe 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 theeye when it views objects with air as its medium.

However, when our eyes are underwater, thelight will no longer be travelling through an air-eye interface, rather it willbe through the water-eye interface. Water’s refractive index is 1.33, which issimilar to the eye’s refractive index (“RefractiveIndex.INFO.”).

Therefore,   This clearly shows that the image formsbehind the eye and not directly on it, which is why everything is out of focuswhen viewed without a protective device such as goggles.    Fig. 4 a) shows the light focusing behindthe eye from a water-eye interface b) shows how an air pocket corrects for thisproperty (Heath 9) Goggles provide a pocket of air directlyin front the eye, allowing light to be refracted through the air-eye interfaceinstead of the water-eye interface. Aside from simply keeping water out of oureyes, goggles play an important role in allowing divers to observe objectsclearly underwater.  These physics properties are only the tipof the iceberg when it comes to diving, yet these are the ones that mostdirectly affect divers. Divers should never hold their breath, wear theappropriate attire, and bring their diving masks for them to dive safely andcomfortably. These are all the consequences of the different physics thatoccurs underwater, yet all of them have been overcome safely due to the diver’sunderstanding of their environment and adequate preparation.

Even now, peopleare developing better equipment for divers to stay in the water morecomfortable, deeper, longer, and all the more comfortable.

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