Lecture 18. Basic Physics and Chemistry. Dmitriy ...leykekhman/courses/...Basic Physics and Chemistry. Dmitriy Leykekhman Spring 2010 ... 100 elements in the universe. I Atomic number

MATH 1050QMathematical 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

Basic Physics and Chemistry

I Matter is anything that takes up space

I Atoms are the smallest units of matter that are capable of enteringinto chemical reaction. An atom is made of a nucleus, consisting ofprotons and neutrons, and of electrons which surround and orbitthe nucleus.

I Elements are collections of atoms all of which contain the samenumber of both protons and electrons. Elements are the simplestsubstances that can be isolated by chemical means. There are over100 elements in the universe.

I Atomic number of an atom is the total number of protons in itsnucleus. In a normal atom this is equal to the total number ofelectrons. The atomic number determines the chemical properties ofan element.





















I Isotopes are atoms that vary from one another only in the numberof neutrons they contain. Thus isotopes have the same atomicnumber and therefore the same chemical properties, although theymay have different physical properties. For example, some isotopesmay be radioactive while others may not be so.

I Atomic weight of a single atom is the total number of protons plusthe total number of neutrons. The atomic weight of an element isthe ”weighted average” of the atomic weights of all isotopes of itsatom, 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 plainatom.

I Molecular weight of a molecule is the sum of atomic weights ofindividual atoms making up the molecule.





















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 ofwater is 62.4 lb/ft3.

I Specific gravity: of a substance is the ratio of its density to thedensity of water. Has no units.Example:

Specific gravity (rock) =density of rock

density of water=

200lbs/ft3

62.4lbs/ft3= 2.5



Three states: solid, liquid, gas

I Density: mass per unit volume.For example 1 ft3 of water weights 62.4 lb, hence the density ofwater is 62.4 lb/ft3.

I Specific gravity: of a substance is the ratio of its density to thedensity of water. Has no units.Example:

Specific gravity (rock) =density of rock

density of water=

200lbs/ft3

62.4lbs/ft3= 2.5



I Evaporation: is the process under which usually a liquid substanceturns to gas.

I This is accomplished when the liquid’s molecules driven by theirkinetic energy escape from the liquid space into vapor space.Evaporation occurs as molecules near the surface have sufficientkinetic energy to break through the surface.

I Rate of evaporation increases with temperature.

I Rate of evaporation is proportional to surface area.














Effect of surface area on evaporation rate

figure 4.2 from the textbook.D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info – 7

Effect of surface area on evaporation rate

figure 4.3 from the textbook.D. Leykekhman - MATH 1050Q Mathematical Modeling in the Environment Course info – 8

Vapor pressure

figure 4.4 from the textbook.


Vapor pressure

I When the vapor space is saturated with the substance’s moleculesevaporation ceases and system is said to be in equilibrium

I Volatile material is material that quite easily evaporates

I Vapor pressure is the pressure added to the vapor by the additionof substance’s molecules to the existing air molecules, at themoment the system reaches equilibrium.


Boiling

figure 4.5 from the textbook.


Boiling

I When heat is applied to a liquid substance and it evaporates, thevapor pressure rises. The temperature at which the vapor pressurereaches the atmospheric pressure is called the boiling point of thesubstance.

I At boiling vapor pressure in higher than atmospheric pressure andchemical can enter vapor form from throughout the liquid.

I The amount of heat, measured in calories, it takes to evaporate 1gram of a given liquid is called the heat of vaporization of thatliquid.


Boiling

Some chemicals have such high vapor pressure that they boil at normalroom temperature. Such chemicals are stored in liquid form inpressurized containers. If such a container ruptures, it loses pressure andthe chemical inside it comes to a rapid boil filling the container withfoam, which is a mixture of gas and fine liquid droplets.

Flash boiling is the sudden vaporization of liquid caused by loss ofpressure.


Class problem on using ALOHA

In a small industrial park outside of Baton Rouge, Louisiana, a500-gallon, 4-foot-diameter vertical talk contains liquid benzene. OnAugust 20, 2000, at 10:30 p.m. local time, a security guard discoveredthat liquid is leaking out of the talk through a 6-inch circular hole located10 inches above the bottom of the tank. He also sees that the liquid isflowing onto grassy field west of the industrial park. The guard thinksthat the tank had just been filled that evening.

The temperature on scene is 80◦ F, with the wind from the East at 7knots (as measured at a height of 10 meters by a fixed meteorologicaltower at the site). The sky is more than half covered by clouds and thehumidity is about 75 percent. There is no inversion.

The Local Emergency Planning committee (LEPC) has indicated that theLevel of Concern (LOC) for this product is 10 parts per million (ppm).


Class problem on using ALOHA (cont)

Run ALOHA for the above case scenario and answer the followingquestions:

1. what is the downwind toxic vapor-cloud hazard distance for the LOCset by LEPC?

2. A crew of workers is supposed to start a plant related job, at alocation of 800 yards downhill form the industrial park, and at time11:15 p.m. Is it safe for them to start their job on time? If not, howlong do you recommend they should wait before it is safe to startwork at this particular location?

3. In running ALOHA for the original scenario we assumed the windblows from the east. This meant that the cloud vapor was blownwest into the grassy filed, and therefore the ground roughness couldbe considered to be ”open country”. Assume now that the windblows from the west. In what direction would the vapor-cloud blow?How would the downwind toxic vapor-cloud hazard distance beaffected by this change?


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Lecture 18. Basic Physics and Chemistry. Dmitriy ...leykekhman/courses/...Basic Physics and Chemistry. Dmitriy Leykekhman Spring 2010 ... 100 elements in the universe. I Atomic number