And the surface volume of air that will supply 5 cubic feet at 75 feet is: P1V1 = P2V2 3.27 ata x 5 ft3 = 1 ata x V2 V2 = 16.35 ft3 You can use your cylinder specifications to find how much pressure will be used from your cylinder to supply a given volume of air. For example, how many psi will be used to supply the above 16.35 cubic feet if 3,000 psi (or 3,014.7 psia) is 80 cubic feet in your cylinder. This is a simple conversion, not a Boyle’s law problem. Pressure used = Volume used x Pressure full Volume full Pused = 16.35 ft3 x (3,015 psia) 80 ft3 Pused = 616 psi Charles’ Law The second gas law expresses the relationship between the volume of a fixed amount of gas and the absolute temperature. About 1787, J.-A.-C. Charles, a French experimenter known to his contemporaries primarily for his contributions to the art of ballooning, recognized that the volume occupied by several gases was proportional to their temperature, but Charles did not publish his findings. In 1802, Joseph-Louis Gay-Lussac undertook research on the thermal expansion of gases and considerably refined on Charles observations using improved experimental techniques and mathematical rigor. Gay Lussac concluded that equal volumes of all gases expand equally with the same increase in temperature. He found that over the temperature range from 0°C to 100°C gases expanded by about 1/270th of the volume at 0°C for each degree rise in temperature. Similar, though less accurate work was carried out by Dalton at about the same time. Today, the law of thermal expansion of gases bears the name of its first observer. Charles’ law states: “For any gas at a constant pressure, the volume of the gas is directly proportional to its absolute temperature.” Expressed as a working formula, Charles’ law is: V1 = Chapter 3- Diving Physics V2 T1 T2 where T and V are the absolute temperature and the volume for any two sets of conditions. The fact that absolute temperatures must be used is reflected in Gay- Lussac’s finding that the volume changes by about 1/270th for each degree Celsius. When solving problems using Charles’ law, degrees Celsius must be converted to kelvin by adding 273, and degrees Fahrenheit must be converted to degrees Rankine by adding 460. Sample problems: SI/metric A small helium-filled balloon contains 15,000 liters of helium on a cold morning when the air temperature is 5°C. The balloon stands unlaunched in the sun all morning, and the temperature rises to 25°C. What will be the volume of helium in the balloon (which does not reach full expansion during the heating)? Using Charles’ law (and absolute temperatures): V1 = V2 T1 T2 15,000 L = V2 (5°C + 273°) (25°C + 273°) V2 = 15,000 L x (298 k / 278 k) = 16,079 L U.S./Imperial An inverted one gallon bottle immersed in a cauldron of 68°F water is half full of air. If the water is heated to 180°F, what will be the volume of the air in the bottle? Again, Charles’s law is applicable, and the temperatures should be converted from Fahrenheit to Rankine: 0.5 gallon = V2 (68°F + 460°) (180°F + 460°) V2 = 0.5 gallon (640°R / 528°R) = 0.61 gallons Amontons’ Law Generally more relevant to scuba diving would be an equation relating pressure to absolute temperature. Diving Physics 89
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