Air Pollution: Particulate Matter Purpose We will use this lab to develop an understanding of how ne, airborne, particulate matter is measured by industry and regulators. We will use functions and integrals to understand how aerosol concentrations are modeled, and we will use numerical methods of computing integrals to make the connection between the theory and data. Preview Scientists, public health advocates, envi- ronmentalists, and Environmental Protection Agency regulators are concerned with airborne ne particulate matter (PM) for two reasons: PM is one of several pollutants that combine to create smog, thereby limiting visibility and obscuring scenic vistas; and inhalation of PM contributes to a variety of respiratory ilhiesses. Terminology Although we speak of haze, dust, and smoke as different atmospheric phenomena, all of these things are caused by particles in the air. The particles may be solid or liquid, and they may be spherical or irregular in shape. Nevertheless, all of these airborne elements are classied as aerosols by environmental scientists. Thus, we will be speaking of measuring aerosols in the atmosphere. Measuring Particulates The aerosols in the atmosphere over a city generally have a great variety of sizes of particles: they typically range from 10 angstroms (10A: 10 . 1010 m = 109 m) to 100 microns (100 ,um = 100 . 106 m = 104 m) in size. But the effect on our lives is not simple. Indeed, it is typically neither the largest nor the smallest particles which are of most concern in our breathing; rather there is an \"optimal\" range of sizes, which is a mid-sized range, that causes the greatest problems for our lungs. This issue of the size of the particles has motivated scientists to use the diameter of the particles both in their measurements and in their analyses. If a particle is spherical, \"diameter\" makes sense. For irregular particles, the notion of diameter has to be dened carefully. In this case, scientists dene the diameter of the particle to be that which a spherical particle of the same substance would have to have to exhibit similar atmospheric properties. Exercise. Suppose a particle is in the shape of cube, which measures 1.2 microns on each side. For this exercise, assume that the volume is the only signicant environmental property of the particle. What is the \"diameter\" of this particle? Part 2: The Size Distribution Function Because the number of di'erent diameters of particles in a polluted atmosphere can be so large, scientists assume that the variation in diameters of particles is continuous. When scientists make measurements of aerosols, they can measure, for a typical cubic centimeter of air, the number of particles that fall within a small range of diameters. This method of measurement is more efcient and practicable than trying to measure the quantity of every size particle present. Let 30 represent the diameter of particles in an atmosphere. Using the previously stated variation in sizes, we note that typically 10A5p5100um. Let N (p) be a function that expresses the number of particles of diameter less than or equal to p, contained in a cubic centimeter of air over a xed location. The derivative of this function, 6+: is called the size distribution function for aerosols. The approximation of this derivative, 31:, would involve the measurement of how many particles in the size range [p, p + Ap] are in a cubic centimeter of air. Here we have the link between the continuous model and the data. What scientists can measure is AN for various intervals of p. This measurement is practicable because a range of sizes, rather than a particular size, can be ltered and measured. After scientists have the measurements of AN, they can compute and tabulate values of [Iig. If we have values of 31:: then using the approximation AAg x Q we can estimate the number of particles in a cubic tip 3 centimeter of air. 1. Explain the meaning of the integral I: % tip. 2. When the EPA sets a standard for ne particulate matter being emitted into the atmosphere, the Agency species a diameter, p; then any emission must be ltered for particles of diameter greater than or equal to p. Write down an integral that represents the number of particles that the current standard of 10 ,um would cause to be removed from the air. 3. Based on emerging scientic evidence that the smaller particles are dangerous because they lodge deep within the lungs, the EPA announced in the Spring of 1997 its intent to lower the regulatory standard from 10 pm to 2.5 pm. Write down an integral that represents the number of additional particles (per cm3) that would be removed if the standard were changed from 10 pm to 2.5 pm