MATH 1050Q Mathematical Modeling in the Environment

Transcription

1 MATH 1050Q Mathematical Modeling in the Environment Lecture 18. Basic Physics and Chemistry. Dmitriy Leykekhman Spring 2010 D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 1

2 Basic Physics and Chemistry Matter is anything that takes up space D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 2

3 Basic Physics and Chemistry Matter is anything that takes up space Atoms are the smallest units of matter that are capable of entering into chemical reaction. An atom is made of a nucleus, consisting of protons and neutrons, and of electrons which surround and orbit the nucleus. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 2

4 Basic Physics and Chemistry Matter is anything that takes up space Atoms are the smallest units of matter that are capable of entering into chemical reaction. An atom is made of a nucleus, consisting of protons and neutrons, and of electrons which surround and orbit the nucleus. Elements are collections of atoms all of which contain the same number of both protons and electrons. Elements are the simplest substances that can be isolated by chemical means. There are over 100 elements in the universe. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 2

5 Basic Physics and Chemistry Matter is anything that takes up space Atoms are the smallest units of matter that are capable of entering into chemical reaction. An atom is made of a nucleus, consisting of protons and neutrons, and of electrons which surround and orbit the nucleus. Elements are collections of atoms all of which contain the same number of both protons and electrons. Elements are the simplest substances that can be isolated by chemical means. There are over 100 elements in the universe. Atomic number of an atom is the total number of protons in its nucleus. In a normal atom this is equal to the total number of electrons. The atomic number determines the chemical properties of an element. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 2

6 Basic Physics and Chemistry Isotopes are atoms that vary from one another only in the number of neutrons they contain. Thus isotopes have the same atomic number and therefore the same chemical properties, although they may have different physical properties. For example, some isotopes may be radioactive while others may not be so. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 3

7 Basic Physics and Chemistry Isotopes are atoms that vary from one another only in the number of neutrons they contain. Thus isotopes have the same atomic number and therefore the same chemical properties, although they may have different physical properties. For example, some isotopes may be radioactive while others may not be so. Atomic weight of a single atom is the total number of protons plus the total number of neutrons. The atomic weight of an element is the weighted average of the atomic weights of all isotopes of its atom, relative to their prevalence in nature. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 3

8 Basic Physics and Chemistry Isotopes are atoms that vary from one another only in the number of neutrons they contain. Thus isotopes have the same atomic number and therefore the same chemical properties, although they may have different physical properties. For example, some isotopes may be radioactive while others may not be so. Atomic weight of a single atom is the total number of protons plus the total number of neutrons. The atomic weight of an element is the weighted average of the atomic weights of all isotopes of its atom, relative to their prevalence in nature. Molecules are group of atoms bonded together by shared electrons. Most substances are made up of molecules rather then just plain atom. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 3

9 Basic Physics and Chemistry Isotopes are atoms that vary from one another only in the number of neutrons they contain. Thus isotopes have the same atomic number and therefore the same chemical properties, although they may have different physical properties. For example, some isotopes may be radioactive while others may not be so. Atomic weight of a single atom is the total number of protons plus the total number of neutrons. The atomic weight of an element is the weighted average of the atomic weights of all isotopes of its atom, relative to their prevalence in nature. Molecules are group of atoms bonded together by shared electrons. Most substances are made up of molecules rather then just plain atom. Molecular weight of a molecule is the sum of atomic weights of individual atoms making up the molecule. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 3

10 D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 4

11 Physical Properties of Matter Three states: solid, liquid, gas Density: mass per unit volume. For example 1 ft 3 of water weights 62.4 lb, hence the density of water is 62.4 lb/ft 3.. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 5

12 Physical Properties of Matter Three states: solid, liquid, gas Density: mass per unit volume. For example 1 ft 3 of water weights 62.4 lb, hence the density of water is 62.4 lb/ft 3. Specific gravity: of a substance is the ratio of its density to the density of water. Has no units. Example: Specific gravity (rock) = density of rock density of water = 200lbs/ft3 62.4lbs/ft 3 = 2.5. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 5

13 Physical Properties of Matter Evaporation: is the process under which usually a liquid substance turns to gas. This is accomplished when the liquid s molecules driven by their kinetic energy escape from the liquid space into vapor space. Evaporation occurs as molecules near the surface have sufficient kinetic energy to break through the surface. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 6

14 Physical Properties of Matter Evaporation: is the process under which usually a liquid substance turns to gas. This is accomplished when the liquid s molecules driven by their kinetic energy escape from the liquid space into vapor space. Evaporation occurs as molecules near the surface have sufficient kinetic energy to break through the surface. Rate of evaporation increases with temperature. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 6

15 Physical Properties of Matter Evaporation: is the process under which usually a liquid substance turns to gas. This is accomplished when the liquid s molecules driven by their kinetic energy escape from the liquid space into vapor space. Evaporation occurs as molecules near the surface have sufficient kinetic energy to break through the surface. Rate of evaporation increases with temperature. Rate of evaporation is proportional to surface area. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 6

16 Effect of surface area on evaporation rate D. Leykekhman figure - MATH Qfrom Mathematical the Modeling textbook. in the Environment Course info 7

17 Effect of surface area on evaporation rate D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 8

18 Vapor pressure figure 4.4 from the textbook. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 9

19 Vapor pressure When the vapor space is saturated with the substance s molecules evaporation ceases and system is said to be in equilibrium Volatile material is material that quite easily evaporates Vapor pressure is the pressure added to the vapor by the addition of substance s molecules to the existing air molecules, at the moment the system reaches equilibrium. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 10

20 Boiling figure 4.5 from the textbook. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 11

21 Boiling When heat is applied to a liquid substance and it evaporates, the vapor pressure rises. The temperature at which the vapor pressure reaches the atmospheric pressure is called the boiling point of the substance. At boiling vapor pressure in higher than atmospheric pressure and chemical can enter vapor form from throughout the liquid. The amount of heat, measured in calories, it takes to evaporate 1 gram of a given liquid is called the heat of vaporization of that liquid. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 12

22 Boiling Some chemicals have such high vapor pressure that they boil at normal room temperature. Such chemicals are stored in liquid form in pressurized containers. If such a container ruptures, it loses pressure and the chemical inside it comes to a rapid boil filling the container with foam, which is a mixture of gas and fine liquid droplets. Flash boiling is the sudden vaporization of liquid caused by loss of pressure. D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 13

23 Class problem on using ALOHA In a small industrial park outside of Baton Rouge, Louisiana, a 500-gallon, 4-foot-diameter vertical talk contains liquid benzene. On August 20, 2000, at 10:30 p.m. local time, a security guard discovered that liquid is leaking out of the talk through a 6-inch circular hole located 10 inches above the bottom of the tank. He also sees that the liquid is flowing onto grassy field west of the industrial park. The guard thinks that the tank had just been filled that evening. The temperature on scene is 80 F, with the wind from the East at 7 knots (as measured at a height of 10 meters by a fixed meteorological tower at the site). The sky is more than half covered by clouds and the humidity is about 75 percent. There is no inversion. The Local Emergency Planning committee (LEPC) has indicated that the Level of Concern (LOC) for this product is 10 parts per million (ppm). D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 14

24 Class problem on using ALOHA (cont) Run ALOHA for the above case scenario and answer the following questions: 1. what is the downwind toxic vapor-cloud hazard distance for the LOC set by LEPC? 2. A crew of workers is supposed to start a plant related job, at a location of 800 yards downhill form the industrial park, and at time 11:15 p.m. Is it safe for them to start their job on time? If not, how long do you recommend they should wait before it is safe to start work at this particular location? 3. In running ALOHA for the original scenario we assumed the wind blows from the east. This meant that the cloud vapor was blown west into the grassy filed, and therefore the ground roughness could be considered to be open country. Assume now that the wind blows from the west. In what direction would the vapor-cloud blow? How would the downwind toxic vapor-cloud hazard distance be affected by this change? D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info 15