Basic Geometry

Rain Gauge

A rain gauge / Udometer / Pluviometer / Ombrometer is a type of instrument used to gather and measure the amount of liquid precipitation over a set period of time.

Standard rain gauge

A standard rain gauge consists of a funnel emptying into a graduated cylinder of 2 cm in diameter, that fits inside a larger container of 20 cm in diameter and 50 cm in height.

When measurements are taken, the height of the water in the small cylinder is measured.  Excess water overflowed into the larger container is measured too to get a total rainfall. 

General practice is to examine the gauge daily; to measure the water, if any; and to enter the record at once.

Rain is measured in units of length per unit time, typically in millimeters per hour.  One millimeter of rainfall is the equivalent of one liter of water per square meter.

Other types of rain gauges :

1. Weighing precipitation gauge

2. Tipping bucket rain gauge

3. Optical rain gauge

4. Acoustic rain gauge

Raindrops

Raindrops have sizes ranging from 0.1mm – 0.9 mm diameter, above which they tend to break up.   The biggest raindrops ever recorded was 10 mm diameter.

	Drizzle Size : < 0.5 mm  velocity : 2 ms-1
	Cloud droplets size : 0.5-  2.0 mm shape : spherical
	Normal drain drops size : 2.0 – 5.0 mm shape : oblate
	Large drain drops size : > 5.0 mm shape : hamburger buns / parachutes velocity : 9 ms-1
Source : wikipedia	contrary to popular belief, raindrops does not resemble a teardrop.

Marker Pen

Paint markers are permanent markers used to write on a variety of surfaces, eg steel, rubber, timber, plastic, etc.  The  ink is an oil-based paint and generally requires shaking before use.

Permanent markers are porous pens used to writ on smooth surface such as glass, plastic, wood, metal and stone.
The ink comprises a main carrier solvent, a glyceride, a pyrrolidone, a resin and a colorant, making it waterproff.  The marks can be removed by acetone, xylene, toloune, isopropyl alcohol, or ethyl acetate.

Permanent marker was invented in 1952 by Sidney Rosenthal.

A Whiteboard marker is for temporary writing on slick, non-porous writing surface, eg. OHP, whiteboards, glass etc.

Whiteboard marker was invented  by Jerry Woolf of Techform Laboratories.  
It was later patented and produced by Pilot Pen in the 1960s.

Highlighters are permanent markers used to highlight and cover over existing writing while still leaving the writing readable.
A highlighter fluorescent colour is coloured by pyranine.

Highlighter was first introduced in 1963 by Carter's Ink Company.

Water

Systematic Naming

The accepted IUPAC name of water is oxidane (H₂O) or simply water.

The simplest and best systematic name of water is hydrogen oxide.

The polarized form of the water molecule, H⁺OH^-, is also called hydron hydroxide by IUPAC nomenclature.

Dihydrogen monoxide (DHMO) is an overly pedantic naming of water.  Other systematic names for water include hydroxic acid, hydroxylic acid, and hydrogen hydroxide. Both acid and alkali names exist for water because it is amphoteric (able to react both as an acid or an alkali). While these names are technically not incorrect, none of them are used widely.

Electrical Properties

Dipole

Water is 1 molecule of oxygen covalently bonded to 2 hydrogen atoms, forms an angle ( 104.5° ), with H at the tips and O at the vertex.

Since O has a higher electronegativity than H, the side of the molecule with O has a partial negative charge.  An object with such a charge difference is called a dipole.   The charge differences cause water molecules to be attracted to each other and to other polar molecules.  This attraction contributes to hydrogen bonding, and explains many of the properties of water, eg. universal solvent, pH, adhesion, cohesion, capillary action, electric conductivity…   

Hydrogen bonding

A water molecule can form a maximum of 4 hydrogen bonds, because it can accept 2 and donate 2 hydrogen atoms. 

In water local tetrahedral order due to the 4 hydrogen bonds gives rise to an open structure and 3-dimensional bonding network, resulting in the anomalous decrease of density when cooled below 4°C.

Hydrogen bonding is responsible for a number of water’s physical properties, eg. high melting point, high boiling points, large specific heat capacity, large specific heat of vaporization, surface tension & capillary waves, density …

Physical Properties

Taste & Odor

Water is a tasteless, odorless liquid at standard temperature and pressure.

Transparency

Water is transparent to visible light, near ultraviolet light, and far-red light, but it absorbs most ultraviolet light, infrared light and microwaves. 

Most photoreceptors and photosynthetic pigments utilize the portion of the light spectrum that is transmitted well through water.  Thus aquatic plants can live within the water because sunlight can reach them.

Colour

The very weak onset of absorption in the red end of the visible spectrum lends water its intrinsic blue hue.

Density

The density of water is approximately 1 gram per cm³.   Yet it is very inconsistent. 

Although it is dependent on its temperature, the relation is not consistent.  At high temperature, it is less dense.  When it cooled from room temperature, the density increases.  At approximately 4°C, pure water reaches its maximum density.   

Upon freezing, the density of water decreases by about 95%.  Thus, the less denser solid water will float on denser liquid form.   

The reason of this is the water molecule forming hexagonal Ice l_h formation.

These properties of water have important consequences in its role in the Earth’s ecosystem.  Water at 4°C will accumulate at the bottom of fresh water lakes. Ice will floats over the water surface, creating a blanket which prevent loss of heat of the liquid water beneath.  Thus it is unlikely a deep lake will freeze completely, thus help preserve aquatic life.

Surface Tension

Water has a high surface tension of 72.8 mN/m at room temperature, cause by the dipolar interactions, the highest of the non-metallic liquids.  

The effects of surface tension can be seen with ordinary water :

-         beading of water on  sorption-free surface ( non-adsorbent and non-absorbent, eg. polyethylene ).  Surface tension give water their near-spherical shape, because a sphere has the smallest possible surface are to volume ratio.

-         formation of drops.

-         flotation of object denser than water occurs when the object is non-wettable and its weight is small enough to be borne by the forces arising from surface tension.

-         separation of oil and water

-         tears of wine

-         emulsions are a type of solution in which droplets of oil suspended in water ( or vice versa ).

Capillary Action

Due to an interplay of the forces of adhesion and surface tension, water is able to flow against gravity where it spontaneously rises in a narrow space such as a thin tube, or in porous material such as paper or cloths.

Examples of capillary actions:

-         kerosene lamp’s wick

-         chromotography

-         water movement in plant’s xylem

Universal Solvent

Water is a good solvent.  Substances that dissolve in water includes : salts, sugars, acids, alkalis, some gases.

However, water cannot dissolve all substances, especially those that are non-polar or hydrophorbic in nature.

Electrical Conductivity

Pure water does not conduct electricity, thus an excellent insulator.  But there are no such pure that it is free of ions, even deionized water.  As water is such a good solvent, it  almost always has some solute dissolved in it. 

pH

Pure water is pH neutral, that is pH 7.0. 

But since there are no such pure water, as there are a lot of substances that dissolve easily in water.  It is thus, water’s pH is very dependent on dissolved chemicals and minerals, as does it changes over time.

Normally, water pH is < 7.0.   That explains metals rust upon contact with water.  Surface water are mostly acidic.

Water with pH > 7.0 is considered basic.  Sea water is basic in nature.

Water with pH > 8.5 is considered hard water.  Hard water contains high mineral content, especially Ca²⁺ and Mg²⁺.  Hard water is difficult to suds – difficult to produce soap bubbles.  It also forms deposits that clog plumbing.

High Boiling Point

Boiling point is when a substance reach a temperature at which the liquid state of the substance change to vapor, under atmospheric pressure.  Water has a high boiling point ( 100°C ) for its strong hydrogen bonding.  High boiling point means water is not easily vaporized by heat, thus a stable medium for living organism.

Specific Heat Capacity & Heat of Vaporization

Water has the 2^nd highest specific heat capacity of all known substances, after ammonia, as well as high heat of vaporization, both of which are a result of the extensive hydrogen bonding between its molecules.

Specific heat capacity is the amount of energy required to change a substance’s temperature by a given amount. 

Ice’s specific heat capacity at -10°C is about 2.05 J•g^-1•K^-1.

Steam’s specific heat capacity at 100°C is about 2.08 J•g^-1•K^-1.

Heat of vaporization refers to amount of energy required to transform a given quantity of a substance into a gas at a given pressure. 

Water’s heat of vaporization is 2257 kJ•kg^-1.

The high specific heat capacity and heat of vaporization of water help to moderate Earth’s climate by buffering large fluctuations in atmosphere temperature.

Colour of Water

Relatively small quantities of waters observed by humans to be colourless.  The fact is, pure water has a light blue colour which become deeper blue as the thickness of the observed samples increases.   Impurities dissolved or suspended in water may give water different coloured appearance.

Liquid water’s intrinsic natural colour may be demonstrated by looking at a white light source through a long pipe, filled with purified water, that is closed at both ends with a transparent window. 

The light turquoise blue is caused by weak absorption in the red part of the visible spectrum.  Absorptions in the visible spectrum are attributed to excitations of the electronic energy states in matter.

The water molecule has 3 fundamental modes of vibration.  There are two O-H stretching vibrations which occure at ca. 3500 cm^-1 and an H-O-H bending vibration at ca. 1640 cm^-1.   Absorption due to these vibrations occurs in the infrared region of the spectrum.

The observed absorption in the visible spectrum is due mainly to 4^th harmonic frequency ( 3^rd overtone ) of O-H bond-stretching vibrations. 4 x 3500 = 14000 cm cm^-1  is equivalent to a wavelength of ca. 715 nm.  The actual absorption maximum occurs at 698 nm. 

Because absorption intensity decreased significantly with each successive overtone, absorption due to the 4^th overtone is very weak, so to see the blue colour the pipe needs to be a meter or more in length and the water be removed any particles that would otherwise cause color to be generated by Rayleigh scattering.

It is a common misconception that in large bodies, such as the oceans, the water’s colour is blue due to the reflection from the sky on its surface.  It is true only when the water surface is extremely still, i.e. mirror-like, and the angle of incidence is high, as water’s reflectivity rapidly approaches near total reflection under these circumstances, as governed by the Fresnel equations.

Optical scattering of unabsorbed light from water molecules as well as from impurities in the water of oceans or lakes back into the atmosphere provides the opportunity to visibly observe the blue color of water from land or airplanes. 

If the oceans owed their colour to the sky, they would be a lighter shade of blue and would be colourless on cloudy days.

Particles and solutes can absorb light.  Green algae in rivers often lend a blue-green colour.  The red sea has occasional bloom of red Trichodesmium erythraeum algae.  Tannins caused rivers to be dark brown.   High concentration of dissolved lime give the water a turquoise colour. 

Slight discoloration is measured in Hazen Units ( HU ). 

The colour of a water sample can be reported as :

1. Apparent colour, colour of the whole water sample, and consists of colour from both dissolved and suspended components

2. True colour, is measured after filtering the water sample to remove all suspended material.

Plastic Identification Code

Seven groups of plastic polymers, each with specific properties, are used worldwide for packaging applications. Each group of plastic can be identified by its Plastic Identification Code ( PIC ). The PIC appears inside a 3-chasing-arrow recycling symbol.

The PIC was introduced by the Society of the Plastic Industry, Inc. which provides a uniform system for the identification of different polymer types and helps recycling companies to separate different plastics for reprocessing




Polyethylene Terephthalate – PET, PETE

Melting Point : 260 °C

Physical Properties : Clarity, strength, toughness, barrier to gas and moisture.

Common Packaging Application : Soft drink/water/salad dressing bottles, peanut butter/, jam jars, etc

High Density Polyethylene - HDPE

Melting Point : 110-120°C

Physical Properties : Stiffness, strength, toughness, resistance to moisture, permeability to gas.

Common Packaging Applications : water pipes, hula-hoop rigns, milk/juice/water bottles, , shapoo/toiletry bottles, etc

Polyvinyl Chloride – PVC

Melting Point : 100-260°C

Physical Properties : versatility, clarity, ease of blending, strength, toughness

Common Packaging Application : juice bottles, cling films, PVC piping, etc




Low Density Polyethylene – LDPE

Melting Point : 80-95°C

Physical Properties : ease of processing, strength, toughness, flexibility, ease of sealing, barrier to moisture

Common Packaging Application : frozen food bags, squeezable bottles, cling films, flexible container lids, etc

Polypropylene – PP

Melting Point : 130-171°C

Physical Properties : strength, toughness, resistance to heat/chemicals/greese/oil, versatile, barrier to moisture

Common Packaging Application : microwaveable wares, kitchenware, yogurt containers, margarine tubs, microwaveable disposable take-away containers, disposable cups, plates, LEGOS, etc.

Polystyrene – PS

Melting Point : 240°C

Physical Properties : versatility, clarity, easily formed

Common Packaging Application : egg cartons, foam peanuts, disposable cups/plates, trays, cutlery, disposable take-away container, etc

Other ( often Polycarbonate -ABS )

Melting Point : 267°C

Physical Properties – dependent on polymers or combination of polymers

Common Packaging Application : beverage bottles, baby milk bottles, electronic casings, etc

Electromagnetic Spectrum

Radio frequency

Radio waves generally are utilized by antennas of appropriate size (according to the principle of resonance), with wavelengths ranging from hundreds of meters to about one millimeter. They are used for transmission of data, via modulation. Television, mobile phones, wireless networking and amateur radio all use radio waves. The use of the radio spectrum is regulated by many governments through frequency allocation.

Radio waves can be made to carry information by varying a combination of the amplitude, frequency and phase of the wave within a frequency band. When EM radiation impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of that conductor by exciting the electrons of the conducting material. This effect (the skin effect) is used in antennas.

Microwaves

The super high frequency (SHF) and extremely high frequency (EHF) of microwaves come next up the frequency scale. Microwaves are waves which are typically short enough to employ tubular metal waveguides of reasonable diameter. Microwave energy is produced with klystron and magnetron tubes, and with solid state diodes such as Gunn and IMPATT devices. Microwaves are absorbed by molecules that have a dipole moment in liquids. In a microwave oven, this effect is used to heat food. Low-intensity microwave radiation is used in Wi-Fi, although this is at intensity levels unable to cause thermal heating.
Volumetric heating, as used by microwaves, transfer energy through the material electro-magnetically, not as a thermal heat flux. The benefit of this is a more uniform heating and reduced heating time; microwaves can heat material in less than 1% of the time of conventional heating methods.
When active, the average microwave oven is powerful enough to cause interference at close range with poorly shielded electromagnetic fields such as those found in mobile medical devices and cheap consumer electronics

Infrared radiation

The infrared part of the electromagnetic spectrum covers the range from roughly 300 GHz (1 mm) to 400 THz (750 nm). It can be divided into three parts:

Far-infrared, from 300 GHz (1 mm) to 30 THz (10 μm). The lower part of this range may also be called microwaves. This radiation is typically absorbed by so-called rotational modes in gas-phase molecules, by molecular motions in liquids, and by phonons in solids. The water in the Earth's atmosphere absorbs so strongly in this range that it renders the atmosphere effectively opaque. However, there are certain wavelength ranges ("windows") within the opaque range which allow partial transmission, and can be used for astronomy. The wavelength range from approximately 200 μm up to a few mm is often referred to as "sub-millimetre" in astronomy, reserving far infrared for wavelengths below 200 μm.

Mid-infrared, from 30 to 120 THz (10 to 2.5 μm). Hot objects (black-body radiators) can radiate strongly in this range. It is absorbed by molecular vibrations, where the different atoms in a molecule vibrate around their equilibrium positions. This range is sometimes called the fingerprint region since the mid-infrared absorption spectrum of a compound is very specific for that compound.

Near-infrared, from 120 to 400 THz (2,500 to 750 nm). Physical processes that are relevant for this range are similar to those for visible light.

Visible radiation (light)

Above infrared in frequency comes visible light. This is the range in which the sun and stars similar to it emit most of their radiation. It is probably not a coincidence that the human eye is sensitive to the wavelengths that the sun emits most strongly. Visible light (and near-infrared light) is typically absorbed and emitted by electrons in molecules and atoms that move from one energy level to another. The light we see with our eyes is really a very small portion of the electromagnetic spectrum. A rainbow shows the optical (visible) part of the electromagnetic spectrum; infrared (if you could see it) would be located just beyond the red side of the rainbow with ultraviolet appearing just beyond the violet end.
Electromagnetic radiation with a wavelength between 380 nm and 760 nm (790–400 terahertz) is detected by the human eye and perceived as visible light. Other wavelengths, especially near infrared (longer than 760 nm) and ultraviolet (shorter than 380 nm) are also sometimes referred to as light, especially when the visibility to humans is not relevant.
If radiation having a frequency in the visible region of the EM spectrum reflects off of an object, say, a bowl of fruit, and then strikes our eyes, this results in our visual perception of the scene. Our brain's visual system processes the multitude of reflected frequencies into different shades and hues, and through this not-entirely-understood psychophysical phenomenon, most people perceive a bowl of fruit.
At most wavelengths, however, the information carried by electromagnetic radiation is not directly detected by human senses. Natural sources produce EM radiation across the spectrum, and our technology can also manipulate a broad range of wavelengths. Optical fiber transmits light which, although not suitable for direct viewing, can carry data that can be translated into sound or an image. The coding used in such data is similar to that used with radio waves

Ultraviolet light

The amount of penetration of UV relative to altitude in Earth's ozone

Next in frequency comes ultraviolet (UV). This is radiation whose wavelength is shorter than the violet end of the visible spectrum, and longer than that of an x-ray.
Being very energetic, UV can break chemical bonds, making molecules unusually reactive or ionizing them (see photoelectric effect), in general changing their mutual behavior. Sunburn, for example, is caused by the disruptive effects of UV radiation on skin cells, which is the main cause of skin cancer, if the radiation irreparably damages the complex DNA molecules in the cells (UV radiation is a proven mutagen). The Sun emits a large amount of UV radiation, which could quickly turn Earth into a barren desert. However, most of it is absorbed by the atmosphere's ozone layer before reaching the surface.

X-rays

After UV come X-rays, which are also ionizing, but due to their higher energies they can also interact with matter by means of the Compton effect. Hard X-rays have shorter wavelengths than soft X-rays. As they can pass through most substances, X-rays can be used to 'see through' objects, most notably diagnostic x-ray images in medicine (a process known as radiography), as well as for high-energy physics and astronomy. Neutron stars and accretion disks around black holes emit X-rays, which enable us to study them. X-rays are given off by stars, and strongly by some types of nebulae.

Gamma rays

After hard X-rays come gamma rays, which were discovered by Paul Villard in 1900. These are the most energetic photons, having no defined lower limit to their wavelength. They are useful to astronomers in the study of high energy objects or regions, and find a use with physicists thanks to their penetrative ability and their production from radioisotopes. Gamma rays are also used for the irradiation of food and seed for sterilization, and in medicine they are used in radiation cancer therapy and some kinds of diagnostic imaging such as PET scans. The wavelength of gamma rays can be measured with high accuracy by means of Compton scattering.

Electromagnetic Wave

Electromagnetic waves were first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.

According to Maxwell's equations, a spatially-varying electric field generates a time-varying magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave.

EM radiation exhibits both wave properties and particle properties at the same. Both wave and particle characteristics have been confirmed in a large number of experiments.

Wave model

A wave consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves the size of buildings to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:

V = f l

where v is the speed of the wave (c in a vacuum, or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.
Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference.
The energy in electromagnetic waves is sometimes called radiant energy

Particle model

Electromagnetic radiation has particle-like properties as discrete packets of energy, or quanta, called photons. The frequency of the wave is proportional to the particle's energy. Because photons are emitted and absorbed by charged particles, they act as transporters of energy. The energy per photon can be calculated from the Planck–Einstein equation:

E = hf
where E is the energy, h is Planck's constant, and f is frequency. This photon-energy expression is a particular case of the energy levels of the more general electromagnetic oscillator whose average energy, which is used to obtain Planck's radiation law, can be shown to differ sharply from that predicted by the equipartition principle at low temperature, thereby establishes a failure of equipartition due to quantum effects at low temperature.
As a photon is absorbed by an atom, it excites an electron, elevating it to a higher energy level. If the energy is great enough, so that the electron jumps to a high enough energy level, it may escape the positive pull of the nucleus and be liberated from the atom in a process called photoionisation. Conversely, an electron that descends to a lower energy level in an atom emits a photon of light equal to the energy difference. Since the energy levels of electrons in atoms are discrete, each element emits and absorbs its own characteristic frequencies.