not ready to embrace the kinetic theory. Finally, about 1860 three scientists, Rudolf Clausius, James Clerk Maxwell, and Ludwig Boltzmann, each developed the kinetic theory mathematically. Its time had come. The kinetic theory of gases rapidly gained acceptance, and it became one of the most important concepts in the growth of modern science. The kinetic theory describes the dynamics of a perfect or ideal gas. Real gases are not “ideal.” They all deviate to some degree from the ideal, but at the temperatures and pressures we encounter in diving the kinetic theory provides a close approximation of the dynamics of gases. The perfect gas model assumes that the gas is composed of infinitesimally small identical molecules in random motion that are separated by very large distances, that no energy is lost in the collisions, and that all transfer of kinetic energy is heat. In the kinetic theory of gases; pressure, volume, and temperature are interrelated. A gas is very elastic. It will compress if pressure is applied. In the absence of an equal resisting pressure, it will expand. The pressure of a gas is the measured impact force of its molecules on a unit area of its container or the measuring device. The force of impact is dependent on the kinetic energy of the molecules of the gas, which in turn is related to the speed and mass of the molecules. If we heat a gas and increase its temperature, we are adding energy to the system, increasing the speed at which the molecules are traveling and the force of the impacts. Pressure also depends on the frequency of impacts, more impacts means more force applied. If we compress a gas and make it denser, we increase the number of molecules in a given volume, the frequency of impacts on a unit area increases, and the pressure is higher. The Ideal Gas Laws describe the interrelation of pressure, volume, and temperature. They were formulated experimentally prior to the establishment of the kinetic theory of gases, but the basic equation of the kinetic theory can be seen as an amalgamation of the individual gas laws. Boyle’s law, Charles’ law, and Amontons’ law each describe the interrelation of two of the factors. Combined, they are a statement of the General Gas Law. Boyle’s Law In 1660, Sir Robert Boyle published his famous New Experiments Physico-Mechanicall, Touching the Spring of Air and Its Effects in which he showed the elastic properties of air. In the second edition (1662), he developed this discovery into a quantitative relationship (the pressure of a given quantity of gas varies inversely as its volume). Boyle used a J-shaped tube sealed at the end of the short leg. He added mercury to the tube until the “U” was sealed and the height of mercury in each leg was equal. Adding more mercury increased the weight and pressure of the mercury on the trapped column of air, and the height of the air column shrank. Boyle reasoned that the heights of the mercury and air columns stabilized when the pressure of the air equaled the pressure of the mercury on the air. Measuring the height of the column of mercury over the decreasing column of air, Boyle was able to determine that the product of the pressure on the air and the volume of the air was a constant. Expressed mathematically: PV = k Boyle’s law states: “For any gas at a constant temperature, the volume of the gas is inversely proportional to the pressure.” Expressed as a working formula for a constant temperature, Boyle’s law is: P1V1 = P2V2 where P and V are the absolute pressure and the volume for any two sets of conditions. The product of the pressure and volume under the first set of conditions will be equal to the product of the pressure and volume under the second set of conditions. In 1676 Edme Mariotte, a Frenchman, independently discovered the relation of pressure and gas volume and went further, noting that the law holds only if the temperature is held constant. In France the law is called Mariotte’s law. Since any change in volume of a quantity of gas changes the density in the opposite direction (density = mass per unit volume), a corollary to Boyle’s law is that NAUI Master Scuba Diver 86 Diving Physics
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