An adiabatic system is one in which no heat is added or removed.6For an ideal gas (see Real and Ideal Gases), the following rela-tionship holds:
Cv ln (T2÷ T1) = −R ln (V2÷ V1 ) where Cv= heat capacity at constant volume, ln = natural logarithm, T = absolute tempera-tures at condition 1 or 2, R = universal gas constant (see later), and V = volume at con-dition 1 or 2.
This equation can be used to calculate the temperature change following an adiabatic change in volume. The equation indicates that temperature will increase during com-pression and decrease on expansion of an ideal gas. When air is compressed during the filling of a compressed gas cylinder, the tem-perature rises and the cylinder becomes hot.
This increase in temperature can be as much as 1500°F during rapid compressions. In the presence of hydrocarbon contaminants, this heat can serve as an energy source for fire or explosion in an oxygen-enriched atmos-phere. When air is rapidly released from a scuba cylinder, either through the direct opening of the valve to release its contents or via the purge valve, the volume of the gas increases and temperature falls. (The adia-batic cooling associated with gas movement driven by high pressure through a tiny orifice Given that dry air has a density of
0.0012 g/mL and water has a density of 1.0 g/mL, estimate the approximate ratio in heat capacity between water and air.
Determine ratio of mass from density:
Ratio = mass 1 mL water = 1.000 g = 833.3 mass 1 mL air 0.0012 g Determine ratio of specific heats:
specific
Ratio =heat water= 1.00 cal/g°C = 3.39 specific 0.2943 cal/g°C heat air
Finally, estimate the ratio: Heat capac-ity = Mass × Specific heat
Approximate heat capacity ratio
= 833.3 × 3.39
= 2824
is called the Joule-Thompson effect.) When a hyperbaric chamber is compressed, temper-ature increases; when pressure is reduced, temperature falls. Most hyperbaric cham-bers used for clinical therapy require heating and cooling systems to maintain constant temperature during changes in pressure.
TEMPERATURE
Daniel Fahrenheit introduced the first reli-able calibration of temperature in 1724. He picked the lowest temperature he could obtain with a mixture of ice, salt, and water and called that his zero point. He next picked the temperature of a healthy man’s blood and arbitrarily gave it a value of 96. Using mercury as the expanding fluid that would mark his thermometer, he found that water would freeze at a temperature of 32 and boil at a temperature of 212 on his scale. His system, the Fahrenheit temperature scale, is still used in the United States. About 12 years later, Anders Celsius proposed a scale that would be based on 100 units between the freezing point and boiling point of water.
The two systems of measurement can be converted using the following expressions:
°F = (1.8 × °C) + 32 or °F = 9/5°C + 32
°C = (°F – 32) / 1.8°C = 5/9 (°F – 32) Two other temperature scales are impor-tant to divers. They are the Rankine (absolute Fahrenheit) and the Kelvin (absolute Celsius).
The significance of these absolute tempera-ture scales is discussed later (see Charles’
Law). By international convention, the defi-nition of absolute temperature is in degrees Kelvin; thus, no degree symbol is used for Kelvin temperatures.
°R (Rankine) = °F + 460 K (Kelvin) = °C + 273
Although these formulas can be used to convert one temperature scale to another, in diving this is rarely done. Divers accustomed to the Fahrenheit scale use °R (°F + 460), and divers familiar with the Celsius scale use K (°C + 273) for problems that require the use of absolute temperature.
LIGHT
Light is a form of energy. It provides the illumination that we use to visually perceive and characterize our surroundings. White light, as first discussed by Isaac Newton, is composed of a number of components, each perceived as a different color. If white light passes through a prism, then these colors, known as the light spectrum, can be seen. The colors from the prism always have the same order: red, orange, yellow, green, blue, indigo, and violet.
The perception of color depends on which components of the light have been reflected or absorbed by the object being observed.
If an object reflects all the colors, it is observed to be white; if no colors are reflected, then the object observed will be black. Other colors result from combinations of reflection and absorption of the various components of light. The propagation of light is influenced by a number of factors, includ-ing absorption, diffusion, refraction, and reflection.
Absorption
Each of the colors in the light spectrum possesses a different energy and wavelength.
Red is the least energetic color, whereas blue is the most energetic form of visible light.
As light moves through water, the water absorbs the components of light. Because red is the least energetic, it is absorbed first.
Each of the colors, in turn, is absorbed as light passes through any appreciable dis-tance in water. In shallow water, only the red colors disappear, and as depth increases, the environment takes on a bluish cast.
Eventually everything visible becomes deep blue, then black. Application of artificial white either from a dive light or a photo-graphic strobe light allows the diver to observe and record true color.
Diffusion
As light moves through water, it interacts at the molecular level with all substances in the water. The result is that light is scattered and moves in random directions. This process is called diffusion. Divers see less light at depth because the total amount of
light available at the surface has been scat-tered by diffusion.
Turbidity refers to the amount of particu-late material in the water. If turbidity is high, then the abundance of suspended material increases the amount of both diffusion and absorption that occurs. The diver sees less light in turbid water.
Refraction
Light travels at different speeds in different substances. Light slows about 25% when it enters water from air. This change in velocity results in a bending of the light path as it changes from air to water. This bending affects light as if it had moved through an optical lens. The alteration in the path of light as a result of changing media is called refrac-tion. The diver’s mask is an air/water interface;
thus, the mask also acts as a lens. One reason why a diver needs a mask is that our eyes have adapted to focus in air. Objects appear blurred underwater because the eyes cannot adjust enough to bring objects into focus in water. One function for the dive mask is to provide an air/eye interface so that the eyes can focus the light. The result of the air/water interface of the mask is that divers perceive objects to be larger (by four thirds) and closer (by one fourth) than they really are. An object 4 ft away from the diver appears as to be only 3 ft away (see Chapter 3).
Reflection
When light waves strike a smooth pol-ished surface, they bounce off the surface much like a billiard ball bounces off the side cushions of a billiard table. The angle formed by the light leaving the polished surface is the same angle as the light striking the surface when measured from a line perpen-dicular to the surface. In the same fashion, a portion of the light striking water is reflected away from the surface. Near sundown, this effect can significantly reduce the amount of ambient light at depth.
SOUND
Sound is a longitudinal pressure wave that moves through a fluid. Mechanical vibrations caused by the pressure waves produce
sound. The ear converts the vibrations to electrical signals that the brain interprets as sound. In air, we can perceive the direction of a sound source by sensing the time delay between the sound energy striking one ear and then the other. The brain processes this time delay to give a direction. Underwater, the velocity of sound is about four times faster than in air, and the time delay between sound energy striking each ear is too small to be perceived.7 Localization of a sound underwater by humans is possible, particu-larly with low-frequency signals, but it is extremely difficult. Divers should consider sound an unreliable directional cue.
PRESSURE
Pressure is defined as a force that acts on a unit area. The force most often encoun-tered by divers is weight. Thus, pressure is measured in terms of a weight per unit area.
The pressure divers must cope with is a result of the weight of the water and atmos-phere above the diver.
The Greek philosopher Empedocles first expressed the belief that air had weight in the fifth century BC. Even Aristotle said,
“Nature abhors a vacuum.” In 1645, Guericke used his newly developed air pump to remove the air from the space defined by two hollow steel hemispheres that had been placed together. Horses pulling on his hemi-spheres could not separate them. Yet, when the air was replaced in the sphere, the hemispheres could easily be separated.
The implication was that some force (later demonstrated to be atmospheric pressure) in the air was capable of holding the spheres together. The first scientific explanation of the weight of air was by the Italian mathe-matician, Evangesta Torricelli (a student of Galileo), in 1643. His experiment was the basis of the modern barometer. Torricelli filled a tube closed on one end with mercury and, after inverting the tube, placed the tube in a dish of mercury. He noted that the mercury did not drain from the tube into the dish. Instead, it remained within the tube.
His explanation was that air had weight. The weight of the air pushing down on the mercury in the dish was equal to the weight of the mercury in the tube. The height of the mercury (760 mm) in the tube was then defined as atmospheric pressure. Equivalent measurements of pressure can be made with
different fluids; mercury was originally chosen because of its high density (specific gravity of 13.6). An equivalent instrument using water (specific gravity of 1.00) would be over 30 ft high.
Gas pressure in cylinders is measured in gauge pressure, which reads zero at 1 atm.
To determine absolute pressure, 1 atm (in the same units as the gauge) must be added to the gauge pressure.
What is the approximate height of a seawater column that corresponds to 760 mm Hg?
Water is less dense; thus, the height will be greater. The heights of liquids in a vertical column are inversely propor-tional to specific gravity (the specific gravity of seawater is 1.0256, the specific gravity of mercury is 13.546).
760 mm Hg = 1.0256 x mm H2O 13.546 x = 10,037.99 mm H2O
10,037.99 mm = 10.04 m = 32.9 ft
Thus, 760 mm Hg (1 atm) corresponds to 33 ft, or 10 m, of seawater (feet of seawater = fsw; meters of seawater = msw). Units of pressure and conversion factors can be found in Appendix 1.
Pressure due to the water surroundings is called hydrostatic or gauge pressure. This is equal to 1 atm of pressure for every 33 ft (10 m) of depth in seawater (34 ft, or 10.3 m, in fresh water). Open bodies of water are also subjected to the weight of the atmos-phere, so the total (absolute) pressure at depth is the sum of the hydrostatic and atmospheric pressures.
Determine hydrostatic and absolute pres-sure at a depth of 78 fsw (23.8 msw) using the definition of hydrostatic pressure:
Hydrostatic pressure = Depth of water Definition of atm Note: Water depth is in units of length;
atm should be expressed in the same units. If depth is in fsw, then 1 atm = 33 fsw; if depth is in ffw, then 1 atm = 34 ffw;
if depth is in msw, then 1 atm = 10.1 msw, or 10 bar.
Substitute:
English Metric Hydrostastic
= 78 fsw 23.8 msw 23.8 msw pressure 33 fsw/atm 10.1 m/atm 10 m/bar Hydrostatic = 2.36 atm 2.36 atm 2.38 bar
pressure
Absolute = Hydrostatic + Atmospheric pressure = 2.36 atm + 1 atm
= 3.36 ata (ata = Atmospheres absolute)
Absolute = 2.38 bar + 1.01 bar = 3.39 bar pressure
An 80 ft3cylinder contains gas at a pres-sure of 3000 psig (pounds per square inch gauge).
Determine absolute pressure using absolute pressure = gauge pressure + atmospheric pressure:
3000 psi + 14.7 psi = 3014.7 psia (lbs/inch2absolute)
A scuba cylinder contains 2400 L at a gauge pressure of 200 bar.
Determine absolute pressure, which corresponds to an absolute pressure of:
200 bar + 1.01 bar = 201.01 bar