After all, our cylinders are relatively constant in volume. (They actually expand slightly when pressurized; see the section on hydrostatic testing in the Equipment chapter.) Guillaume Amontons was a French scientist who lived at the end of the seventeenth century and experimented with barometers and thermometers. In 1702, he observed that for an equal elevation of temperature, the increase in pressure of a gas was in the same proportion. In recognition of his finding, “Amontons’ law” is sometimes used to refer to the formula relating the pressure of a gas to its temperature (with the volume constant), although this is not a formal designation as are Boyle’s law and Charles’ law. Amontons’ law states: “For any gas at a constant volume, the pressure of the gas is directly proportional to its absolute temperature.” Expressed mathematically, Amontons’ law is: P1 = P2 T1 T2 where T and P are the absolute temperature and the absolute pressure for any two sets of conditions. As with Charles’ law, absolute temperatures are to be used, and Celsius or Fahrenheit temperatures must be converted to kelvin or Rankine. Sample problems: SI/metric A cylinder is rapidly filled to 200 bars. When it is taken off the fill station, the temperature of the air in the cylinder is 60°C. The cylinder is set aside and the temperature falls to 20°C. What will be the final pressure? Both absolute temperatures and absolute pressures should be used in solving the problem. Since cylinder pressures are expressed in gauge pressure, an atmosphere of pressure should be added. Using Amontons’ law: P1 = P2 T1 T2 (200 bars + 1 bar) = P2 (60°C + 273°) (20°C + 273°) P2 = 201 bars x (293 k / 333 k) = 177 bars (absolute) The final cylinder (gauge) pressure will be 176 bars. U.S./Imperial The temperature of a fully charged 3000 psi cylinder is increased by one degree, from 68°F to 69°F. What will be the resulting pressure? P1 = P2 T1 T2 (3,000 psig + 14.7 psi) = P2 (68°F + 460°) (69°F + 460°) P2 = 3,014.7 psia x (529°R / 528°R) = 3,020.4 psia, or about 3,006 psig. A rule of thumb in U.S. measure is that cylinder pressure increases or decreases by about 6 psi for each degree Fahrenheit change in temperature. The above solution shows the basis for the rule of thumb, although the amount of change is less at lower pressures. At 2,400 psi the rate is about 5 psi/1°F. Avogadro’s Law One further law relates to the kinetic theory of gases. In 1811 the Italian scientist Amadeo Avogadro published a seminal memoir in which he hypothesized that the number of molecules in any gas is always the same for equal volumes under the same conditions of temperature and pressure. The source of Avogadro’s inspiration was Gay-Lussac’s law on the proportionality of the combining volumes of gases which had been published two years earlier (e.g., two volumes of hydrogen always combine with one volume of oxygen to produce two volumes of water vapor, or as we would say today, 2H2 + O2 = 2H2O). As with the other gas laws, Avogadro’s law is an ideal gas law, but it is approximately valid for real gases at usual temperatures and pressures. Avogadro’s law had to wait for acceptance; it was not until after 1858 when another Italian published a theory of chemistry based on it that Avogadro’s law gained its deserved recognition. Since Avogadro’s law infers that the relative weights of the molecules of any two gases under like conditions are the same as the ratios of their densities, it can be applied directly to determine the molecular weight of a NAUI Master Scuba Diver 90 Diving Physics
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