Download MATH 1050QC Mathematical Modeling in the Environment

MATH 1050QC
Mathematical Modeling in the Environment
Lecture 18. Basic Physics and Chemistry.
Dmitriy Leykekhman
Spring 2009
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Basic Physics and Chemistry
I
Matter is anything that takes up space
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Basic Physics and Chemistry
I
Matter is anything that takes up space
I
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 1050QC Mathematical Modeling in the Environment
Course info
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2
Basic Physics and Chemistry
I
Matter is anything that takes up space
I
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.
I
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 1050QC Mathematical Modeling in the Environment
Course info
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2
Basic Physics and Chemistry
I
Matter is anything that takes up space
I
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.
I
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.
I
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 1050QC Mathematical Modeling in the Environment
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Basic Physics and Chemistry
I
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 1050QC Mathematical Modeling in the Environment
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Basic Physics and Chemistry
I
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.
I
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 1050QC Mathematical Modeling in the Environment
Course info
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3
Basic Physics and Chemistry
I
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.
I
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.
I
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 1050QC Mathematical Modeling in the Environment
Course info
–
3
Basic Physics and Chemistry
I
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.
I
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.
I
Molecules are group of atoms bonded together by shared electrons.
Most substances are made up of molecules rather then just plain
atom.
I
Molecular weight of a molecule is the sum of atomic weights of
individual atoms making up the molecule.
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Physical Properties of Matter
Three states: solid, liquid, gas
I
Density: mass per unit volume.
For example 1 ft3 of water weights 62.4 lb, hence the density of
water is 62.4 lb/ft3 .
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Physical Properties of Matter
Three states: solid, liquid, gas
I
Density: mass per unit volume.
For example 1 ft3 of water weights 62.4 lb, hence the density of
water is 62.4 lb/ft3 .
I
Specific gravity: of a substance is the ratio of its density to the
density of water. Has no units.
Example:
Specific gravity (rock) =
200lbs/ft3
density of rock
=
= 2.5
density of water
62.4lbs/ft3
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Physical Properties of Matter
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Evaporation: is the process under which usually a liquid substance
turns to gas.
I
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 1050QC Mathematical Modeling in the Environment
Course info
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Physical Properties of Matter
I
Evaporation: is the process under which usually a liquid substance
turns to gas.
I
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.
I
Rate of evaporation increases with temperature.
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
Course info
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Physical Properties of Matter
I
Evaporation: is the process under which usually a liquid substance
turns to gas.
I
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.
I
Rate of evaporation increases with temperature.
I
Rate of evaporation is proportional to surface area.
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Effect of surface area on evaporation rate
figure 4.2 from the textbook.
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Effect of surface area on evaporation rate
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Vapor pressure
figure 4.4 from the textbook.
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Vapor pressure
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When the vapor space is saturated with the substance’s molecules
evaporation ceases and system is said to be in equilibrium
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Volatile material is material that quite easily evaporates
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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 1050QC Mathematical Modeling in the Environment
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Boiling
figure 4.5 from the textbook.
D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment
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Boiling
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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.
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At boiling vapor pressure in higher than atmospheric pressure and
chemical can enter vapor form from throughout the liquid.
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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 1050QC Mathematical Modeling in the Environment
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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 1050QC Mathematical Modeling in the Environment
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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 1050QC Mathematical Modeling in the Environment
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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 1050QC Mathematical Modeling in the Environment
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