Dwarf Elliptical Galaxy

Hubble Space Telescope's exquisite resolution has allowed astronomers to resolve, for the first time, hot blue
stars deep inside an elliptical galaxy. The swarm of nearly 8,000 blue stars resembles a blizzard of snowflakes
near the core (lower right) of the neighboring galaxy M32, located 2.5 million light-years away in the
constellation Andromeda.
Hubble confirms that the ultraviolet light comes from a population of extremely hot helium-burning stars at a late
stage in their lives. Unlike the Sun, which burns hydrogen into helium, these old stars exhausted their central
hydrogen long ago, and now burn helium into heavier elements.
The observations, taken in October 1998, were made with the camera mode of the Space Telescope Imaging
Spectrograph (STIS) in ultraviolet light. The STIS field of view is only a small portion of the entire galaxy, which
is 20 times wider on the sky. For reference, the full moon is 70 times wider than the STIS field-of-view. The
bright center of the galaxy was placed on the right side of the image, allowing fainter stars to be seen on the left
side of the image.
Thirty years ago, the first ultraviolet observations of elliptical galaxies showed that they were surprisingly bright
when viewed in ultraviolet light. Before those pioneering UV observations, old groups of stars were assumed to
be relatively cool and thus extremely faint in the ultraviolet. Over the years since the initial discovery of this
unexpected ultraviolet light, indirect evidence has accumulated that it originates in a population of old, but hot,
helium-burning stars. Now Hubble provides the first direct visual evidence.
Nearby elliptical galaxies are thought to be relatively simple galaxies comprised of old stars. Because they are
among the brightest objects in the Universe, this simplicity makes them useful for tracing the evolution of stars
and galaxies.

Early Cosmology

Early Cosmology:
Cosmology is the study of the Universe and its components, how it formed, how its has evolved and what
is its future. Modern cosmology grew from ideas before recorded history. Ancient man asked questions
such as "What's going on around me?" which then developed into "How does the Universe work?", the
key question that cosmology asks.
Many of the earliest recorded scientific observations were about cosmology, and pursue of understanding
has continued for over 5000 years. Cosmology has exploded in the last 10 years with radically new
information about the structure, origin and evolution of the Universe obtained through recent
technological advances in telescopes and space observatories and bascially has become a search for the
understanding of not only what makes up the Universe (the objects within it) but also its overall
architecture.

Modern cosmology is on the borderland between science and philosophy, close to philosophy because it
asks fundamental questions about the Universe, close to science since it looks for answers in the form of
empirical understanding by observation and rational explanation. Thus, theories about cosmology operate
with a tension between a philosophical urge for simplicity and a wish to include all the Universe's features
versus the shire complexitied of it all.
Very early cosmology, from Neolithic times of 20,000 to 100,000 years ago, was extremely local. The
Universe was what you immediately interacted with. Things outside your daily experience appeared
supernatural, and so we call this time the Magic Cosmology.

Later in history, 5,000 to 20,000 years ago, humankind begins to organize themselves and develop what
we now call culture. A greater sense of permanence in your daily existences leads to the development of
myths, particularly creation myths to explain the origin of the Universe. We call this the Mythical
Cosmology.

The third stage, what makes up the core of modern cosmology grew out of ancient Greek, later Christian,
views. The underlying theme here is the use of observation and experimentation to search for simple,
universal laws. We call this the Geometric Cosmology.

The earliest beginnings of science was to note that there exist patterns of cause and effect that are
manifestations of the Universe's rational order. We mostly develop this idea as small children (touch hot
stove = burn/pain). But the extrapolation of a rational order to cosmology requires a leap of faith in the
beginning years of science, later supported by observation and experimentation.

Greek Cosmology

Greek Cosmology
The earliest cosmology was an extrapolation of the Greek system of four elements in the Universe (earth,
water, fire, air) and that everything in the Universe is made up of some combination of these four primary
elements. In a seemlingly unrelated discovery, Euclid, a Greek mathematician, proofed that there are only
five solid shapes that can be made from simple polygons (the triangle, square and hexagon). Plato,
strongly influenced by this pure mathematical discovery, revised the four element theory with the
proposition that there were five elements to the Universe (earth, water, air, fire and quintessence) in
correspondence with the five regular solids.

Each of these five elements occupied a unique place in the heavens (earth elements were heavy and,
therefore, low; fire elements were light and located up high). Thus, Plato's system also became one of the
first cosmological models and looked something like the following diagram:

Like any good scientific model, this one offers explanations and various predictions. For example, hot air
rises to reach the sphere of Fire, so heated balloons go up. Note that this model also predicts some
incorrect things, such as all the planets revolve around the Earth, called the geocentric theory.
Middle Ages
The distinction between what mades up matter (the primary elements) and its form became a medieval
Christian preoccupation, with the sinfulness of the material world opposed to the holiness of the heavenly
realm. The medieval Christian cosmology placed the heavens in a realm of perfection, derived from
Plato's Theory of Forms

Before the scientific method was fully developed, many cosmological models were drawn from religious
or inspirational sources. One such was the following scheme taken from Dante's `The Divine Comedy'.

The political and intellectual authority of the medieval church declined with time, leading to the creative
anarchy of the Renaissance. This produced a scientific and philosophical revolution including the birth of
modern physics. Foremost to this new style of thinking was a strong connection between ideas and facts
(the scientific method).

Since cosmology involves observations of objects very far away (therefore, very faint) advancement in
our understanding of the cosmos has been very slow due to limits in our technology. This has changed
dramatically in the last few years with the construction of large telescopes and the launch of space-based
observatories.

Olber's Paradox

Olber's Paradox:
The oldest cosmological paradox concerns the fact that the night sky should appear as bright as the
surface of the Sun in a very large (or infinite), ageless Universe.

Note that the paradox cannot be resolved by assuming that parts of the Universe are filled with absorbing
dust or dark matter, because eventually that material would heat up and emit its own light.
The resolution of Olber's paradox is found in the combined observation that 1) the speed of light is finite
(although a very high velocity) and 2) the Universe has a finite age, i.e. we only see the light from parts of
the Universe less than 15 billion light years away.
Rationalism:
The main purpose of science is to trace, within the chaos and flux of phenomena, a consistent structure
with order and meaning. This is called the philosophy of rationalism. The purpose of scientific
understanding is to coordinate our experiences and bring them into a logical system.

Thoughout history, intellectual efforts are directed towards the discovery of pattern, system and structure,
with a special emphasis on order. Why? control of the unpredictable, fear of the unknown, and a person
who seeks to understand and discover is called a scientist.
Thoughout history, intellectual efforts are directed towards the discovery of pattern, system and structure,
with a special emphasis on order. Why? control of the unpredictable, fear of the unknown, and a person
who seeks to understand and discover is called a scientist.

Cause+Effect

Cause+Effect:
The foundation for rationalism rests squarely on the principle of locality, the idea that correlated events
are related by a chain of causation.

There are three components to cause and effect:
l contiguity in space
l temporal priority of the cause (i.e. its first)
l necessary connection

The necessary connection in cause and effect events is the exchange of energy, which is the foundation of
information theory => knowledge is power (energy).
Also key to cause and effect is the concept that an object's existence and properties are independent of the
observation or experiment and rooted in reality.

Causal links build an existence of patterns that are a manifestation of the Universe's rational order. Does
the chain of cause and effect ever end? Is there an `Initial Cause'?
Science:
The tool of the philosophy of rationalism is called science. Science is any system of knowledge that is concerned with
the physical world and its phenomena and entails unbiased observations and/or systematic experimentation. In
general, a science involves a pursuit of knowledge covering general truths or the operations of fundamental laws of
nature.

Science is far from a perfect instrument of knowledge, but it provides something that other philosophies often fail to
provide, concrete results. Science is a ``candle in the dark'' to illuminate irrational beliefs or superstitions.

Science does not, by itself, advocate courses of human action, but it can certainly illuminate the possible consequences
of alternative courses. In this regard, science is both imaginative and disciplined, which is central to its power of
prediction.
The keystone to science is proof or evidence/data, which is not to be confused with certainty. Except in pure
mathematics, nothing is known for certain (although much is certainly false). Central to the scientific method is a
system of logic.
Scientific arguments of logic basically take on four possible forms; 1) the pure method of deduction, where some
conclusion is drawn from a set of propositions (i.e. pure logic), 2) the method of induction, where one draws general
conclusions from particular facts that appear to serve as evidence, 3) by probability, which passes from frequencies
within a known domain to conclusions of stated likelihood, and 4) by statistical reasoning, which concludes that, on
the average, a certain percentage of a set of entities will satisfy the stated conditions. To support these methods, a
scientist also uses a large amount of skepticism to search for any fallacies in arguments.

The fact that scientific reasoning is so often successful is a remarkable property of the Universe, the dependability of
Nature.

Scientific Method

Scientific Method:
Of course, the main occupation of a scientist is problem solving with the goal of understanding the Universe. To
achieve this goal, a scientist applies the scientific method. The scientific method is the rigorous standard of procedure
and discussion that sets reason over irrational belief. The process has four steps:
l observation/experimentation
l deduction
l hypothesis
l falsification
Note the special emphasis on falsification, not verification. A powerful hypothesis is one that is actually highly
vulnerable to falsification and that can be tested in many ways.
The underlying purpose of the scientific method is the construction of simplifying ideas, models and theories, all with
the final goal of understanding.

The only justification for our concepts of `electron', `mass', `energy', or `time' is that they serve to represent the
complexity of our experiences. It is an ancient debate on whether humankind invents or discovers physical laws.
Whether natural laws exist independent of our culture or whether we impose these laws on Nature as crude
approximations.
Science can be separated from pseudo-science by the principle of falsifiability, the concept that ideas must be capable
of being proven false in order to be scientifically valid.
Reductionism:
Reductionism is the belief that any complex set of phenomena can be defined or explained in terms of a relatively few
simple or primitive ones.

For example, atomism is a form of reductionism in that it holds that everything in the Universe can be broken down
into a few simple entities (elementary particles) and laws to describe the interactions between them. This idea became
modern chemistry which reduces all chemical properties to ninety or so basic elements (kinds of atoms) and their rules
of combination.
Reductionism is very similar to, and has its roots from, Occam's Razor, which states that between competing ideas, the
simplest theory that fits the facts of a problem is the one that should be selected.
Reductionism was widely accepted due to its power in prediction and formulation. It is, at least, a good approximation
of the macroscopic world (although it is completely wrong for the microscope world, see quantum physics).
Too much success is a dangerous thing since the reductionist philosophy led to a wider paradigm, the methodology of
scientism, the view that everything can and should be reduced to the properties of matter (materialism) such that
emotion, aesthetics and religious experience can be reduced to biological instinct, chemical imbalances in the brain,
etc. The 20th century reaction against reductionism is relativism. Modern science is somewhere in between.
Determinism:
Closely associated with reductionism is determinism, the philosophy that everything has a cause, and that a particular
cause leads to a unique effect. Another way of stating this is that for everything that happens there are conditions such
that, given them, nothing else could happen, the outcome is determined.

Determinism implies that everything is predictable given enough information.
Newtonian or classical physics is rigidly determinist, both in the predictions of its equations and its foundations, there
is no room for chance, surprise or creativity. Everything is as it has to be, which gave rise to the concept of a
clockwork Universe.

Mathematics and Science

Mathematics and Science:
The belief that the underlying order of the Universe can be expressed in mathematical form lies at the heart of science
and is rarely questioned. But whether mathematics a human invention or if it has an independent existence is a
question for metaphysics.
There exists two schools of thought. One that mathematical concepts are mere idealizations of our physical world. The
world of absolutes, what is called the Platonic world, has existence only through the physical world. In this case, the
mathematical world would be though of as emerging from the world of physical objects.

The other school is attributed to Plato, and finds that Nature is a structure that is precisely governed by timeless
mathematical laws. According to Platonists we do not invent mathematical truths, we discover them. The Platonic
world exists and physical world is a shadow of the truths in the Platonic world. This reasoning comes about when we
realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high
degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a
world of pure math.

Mathematics transcends the physical reality that confronts our senses. The fact that mathematical theorems are
discovered by several investigators indicates some objective element to mathematical systems. Since our brains have
evolved to reflect the properties of the physical world, it is of no surprise that we discover mathematical relationships
in Nature.

Galileo's Laws of Motion

Galileo's Laws of Motion:
Galileo Galilei stressed the importance of obtaining knowledge through precise and quanitiative experiment and
observation. Man and Nature are considered distinct and experiment was seen as a sort of dialogue with Nature.
Nature's rational order, which itself is derived from God, was manifested in definite laws.

Aside from his numerous inventions, Galileo also laid down the first accurate laws of motion for masses. Galileo
realized that all bodies accelerate at the same rate regardless of their size or mass. Everyday experience tells you
differently because a feather falls slower than a cannonball. Galileo's genius lay in spotting that the differences that
occur in the everyday world are in incidental complication (in this case, air friction) and are irrelevant to the real
underlying properties (that is, gravity) which is pure mathematical in its form. He was able to abstract from the
complexity of real-life situations the simplicity of an idealized law of gravity.
Key among his investigations are:
l developed the concept of motion in terms of velocity (speed and direction) through the use of inclined planes.
l developed the idea of force, as a cause for motion.
determined that the natural state of an object is rest or uniform motion, i.e. objects always have a velocity,
sometimes that velocity has a magnitude of zero = rest.
l
l objects resist change in motion, which is called inertia.
Galileo also showed that objects fall with the same speed regardless of their mass. The fact that a feather falls slowly
than a steel ball is due to amount of air resistance that a feather experiences (alot) versus the steel ball (very little).

Newtonian Physics

Newtonian Physics:
Newtonian or classical physics is reductionist, holding that all physical reality can be
reduced to a few particles and the laws and forces acting among them. Newtonian
physics is free of spiritual or psychological forces = emphasis on objectivity.
Newton expanded on the work of Galileo to better define the relationship between
energy and motion. In particular, he developed the following concepts:
l the change in velocity of an object is called acceleration, and is caused by a force

l The resistance an object has to changes in velocity is called inertia and is proportional
to its mass
l Momentum is a quantity of motion (kinetic) energy and is equal to mass times
velocity

Key to the clockwork universe concept are the conservation laws in Newtonian physics.
Specifically, the idea that the total momentum of an interaction is conserved (i.e. it is the
same before and after).

Conservation laws allow detailed predictions from initial conditions, a highly
deterministic science.

Newton's Law of Universal Gravitation

Newton's Law of Universal Gravitation:
Galileo was the first to notice that objects are ``pulled'' towards the center of the Earth,
but Newton showed that this same force (gravity) was responsible for the orbits of the
planets in the Solar System.

Objects in the Universe attract each other with a force that varies directly as the product
of their masses and inversely as the square of their distances

All masses, regardless of size, attract other masses with gravity. You don't notice the
force from nearby objects because their mass is so small compared to the mass of the
Earth. Consider the following example:

Newton's development of the underlying cause of planetary motion, gravity, completed
the solar system model begun by the Babylonians and early Greeks. The mathematical
formulation of Newton's dynamic model of the solar system became the science of
celestial mechanics, the greatest of the deterministic sciences.

Although Newtonian mechanics was the grand achievement of the 1700's, it was by no
means the final answer. For example, the equations of orbits could be solved for two
bodies, but could not be solved for three or more bodies. The three body problem
puzzled astronomers for years until it was learned that some mathematical
problems suffer from deterministic chaos, where dynamical systems have
apparently random or unpredictable behavior.

Electricity

Electricity:
The existence of electricity, the phenomenon associated with stationary or moving
electric charges, has been known since the Greeks discovered that amber, rubbed
with fur, attracted light objects such as feathers. Ben Franklin proved the
electrical nature of lightning (the famous key experiment) and also established the
conventional use of negative and positive types of charges.

By the 18th century, physicist Charles Coulomb defined the quantity of electricity
(electric charge) later known as a coulomb, and determined the force law between
electric charges, known as Coulomb's law. Coulomb's law is similar to the law of
gravity in that the electrical force is inversely proportional to the distance of the
charges squared, and proportional to the product of the charges.
By the end of the 18th century, we had determined that electric charge could be
stored in a conducting body if it is insulated from its surroundings. The first of
these devices was the Leyden jar. consisted of a glass vial, partly filled with sheets
of metal foil, the top of which was closed by a cork pierced with a wire or nail. To
charge the jar, the exposed end of the wire is brought in contact with a friction
device.

Modern atomic theory explains this as the ability of atoms to either lose or gain an
outer electron and thus exhibit a net positive charge or gain a net negative charge
(since the electron is negative). Today we know that the basic quantity of electric
charge is the electron, and one coulomb is about 6.24x1018 electrons.
The battery was invented in the 19th century, and electric current and static
electricity were shown to be manifestations of the same phenomenon, i.e. current is
the motion of electric charge. Once a laboratory curiosity, electricity becomes the
focus of industrial concerns when it is shown that electrical power can be
transmitted efficiently from place to place and with the invention of the
incandescent lamp.

The discovery of Coulomb's law, and the behavior or motion of charged particles
near other charged particles led to the development of the electric field concept. A
field can be considered a type of energy in space, or energy with position. A field is
usually visualized as a set of lines surrounding the body, however these lines do
not exist, they are strictly a mathematical construct to describe motion. Fields are
used in electricity, magnetism, gravity and almost all aspects of modern physics.

An electric field is the region around an electric charge in which an electric force
is exerted on another charge. Instead of considering the electric force as a direct
interaction of two electric charges at a distance from each other, one charge is
considered the source of an electric field that extends outward into the
surrounding space, and the force exerted on a second charge in this space is
considered as a direct interaction between the electric field and the second charge.

Magnetism

Magnetism:
Magnetism is the phenomenon associated with the motion of electric charges,
although the study of magnets was very confused before the 19th century because
of the existence of ferromagnets, substances such as iron bar magnets which
maintain a magnetic field where no obvious electric current is present (see below).
Basic magnetism is the existence of magnetic fields which deflect moving charges
or other magnets. Similar to electric force in strength and direction, magnetic
objects are said to have `poles' (north and south, instead of positive and negative
charge). However, magnetic objects are always found in pairs, there do not exist
isolated poles in Nature.

The most common source of a magnetic field is an electric current loop. The
motion of electric charges in a pattern produces a magnetic field and its associated
magnetic force. Similarly, spinning objects, like the Earth, produce magnetic
fields, sufficient to deflect compass needles.
Today we know that permanent magnets are due to dipole charges inside the
magnet at the atomic level. A dipole charge occurs from the spin of the electron
around the nucleus of the atom. Materials (such as metals) which have incomplete
electron shells will have a net magnetic moment. If the material has a highly
ordered crystalline pattern (such as iron or nickel), then the local magnetic fields
of the atoms become coupled and the material displays a large scale bar magnet
behavior.

Electromagnetism

Electromagnetism:
Although conceived of as distinct phenomena until the 19th century, electricity
and magnetism are now known to be components of the unified theory of
electromagnetism.
A connection between electricity and magnetism had long been suspected, and in
1820 the Danish physicist Hans Christian Orsted showed that an electric current
flowing in a wire produces its own magnetic field. Andre-Marie Ampere of France
immediately repeated Orsted's experiments and within weeks was able to express
the magnetic forces between current-carrying conductors in a simple and elegant
mathematical form. He also demonstrated that a current flowing in a loop of wire
produces a magnetic dipole indistinguishable at a distance from that produced by a
small permanent magnet; this led Ampere to suggest that magnetism is caused by
currents circulating on a molecular scale, an idea remarkably near the modern
understanding.
Faraday, in the early 1800's, showed that a changing electric field produces a
magnetic field, and that vice-versus, a changing magnetic field produces an
electric current. An electromagnet is an iron core which enhances the magnetic
field generated by a current flowing through a coil, was invented by William
Sturgeon in England during the mid-1820s. It later became a vital component of
both motors and generators.
The unification of electric and magnetic phenomena in a complete mathematical
theory was the achievement of the Scottish physicist Maxwell (1850's). In a set of
four elegant equations, Maxwell formalized the relationship between electric and
magnetic fields. In addition, he showed that a linear magnetic and electric field
can be self-reinforcing and must move at a particular velocity, the speed of light.
Thus, he concluded that light is energy carried in the form of opposite but
supporting electric and magnetic fields in the shape of waves, i.e. self-propagating
electromagnetic waves.

Electromagnetic Radiation (a.k.a. Light)

Electromagnetic Radiation (a.k.a. Light):
The wavelength of the light determines its characteristics. For example, short
wavelengths are high energy gamma-rays and x-rays, long wavelengths are radio
waves. The whole range of wavelengths is called the electromagnetic spectrum.

Our eyes only see over the following range of wavelengths:

Wave Properties:
Due to its wave-like nature, light has three properties when encountering a
medium:
1) reflection
2) refraction
3) diffraction
When a light ray strikes a medium, such as oil or water, the ray is both refracted
and reflected as shown below:

The angle of refraction is greater for a denser medium and is also a function of
wavelength (i.e. blue light is more refracted compared to red and this is the origin
to rainbows from drops of water)

Diffraction is the constructive and destructive interference of two beams of light
that results in a wave-like pattern

Doppler effect:
The Doppler effect occurs when on object that is emitting light is in motion with
respect to the observer. The speed of light does not change, only the wavelength. If
the object is moving towards the observer the light is ``compressed'' or blueshifted.
If the object is moving away from the observer the light is ``expanded'' or
redshifted.

We can use the Doppler effect to measure the orbital velocity of planets and the
rotation of the planets.

Atomic Theory

Atomic Theory:
The ancient philosopher, Heraclitus, maintained that everything is in a state of flux.
Nothing escapes change of some sort (it is impossible to step into the same river). On
the other hand, Parmenides argued that everything is what it is, so that it cannot
become what is not (change is impossible because a substance would have to
transition through nothing to become something else, which is a logical contradiction).
Thus, change is incompatible with being so that only the permanent aspects of the
Universe could be considered real.
An ingenious escape was proposed in the fifth century B.C. by Democritus. He
hypothesized that all matter is composed of tiny indestructible units, called atoms. The
atoms themselves remain unchanged, but move about in space to combine in various
ways to form all macroscopic objects. Early atomic theory stated that the
characteristics of an object are determined by the shape of its atoms. So, for example,
sweet things are made of smooth atoms, bitter things are made of sharp atoms.
In this manner permanence and flux are reconciled and the field of atomic physics was
born. Although Democritus' ideas were to solve a philosophical dilemma, the fact that
there is some underlying, elemental substance to the Universe is a primary driver in
modern physics, the search for the ultimate subatomic particle.

It was John Dalton, in the early 1800's, who determined that each chemical element is
composed of a unique type of atom, and that the atoms differed by their masses. He
devised a system of chemical symbols and, having ascertained the relative weights of
atoms, arranged them into a table. In addition, he formulated the theory that a
chemical combination of different elements occurs in simple numerical ratios by
weight, which led to the development of the laws of definite and multiple proportions.

He then determined that compounds are made of molecules, and that molecules are
composed of atoms in definite proportions. Thus, atoms determine the composition of
matter, and compounds can be broken down into their individual elements.
The first estimates for the sizes of atoms and the number of atoms per unit volume
where made by Joesph Loschmidt in 1865. Using the ideas of kinetic theory, the idea
that the properties of a gas are due to the motion of the atoms that compose it,
Loschmidt calculated the mean free path of an atom based on diffusion rates. His
result was that there are 6.022x1023 atoms per 12 grams of carbon. And that the typical
diameters of an atom is 10-8 centimeters.
Matter:
Matter exists in four states: solid, liquid, gas and plasma. Plasmas are only found in
the coronae and cores of stars. The state of matter is determined by the strength of the
bonds between the atoms that makes up matter. Thus, is proportional to the
temperature or the amount of energy contained by the matter.

The change from one state of matter to another is called a phase transition. For
example, ice (solid water) converts (melts) into liquid water as energy is added.
Continue adding energy and the water boils to steam (gaseous water) then, at several
million degrees, breaks down into its component atoms.

The key point to note about atomic theory is the relationship between the macroscopic
world (us) and the microscopic world of atoms. For example, the macroscopic world
deals with concepts such as temperature and pressure to describe matter. The
microscopic world of atomic theory deals with the kinetic motion of atoms to explain
macroscopic quantities.
Temperature is explained in atomic theory as the motion of the atoms (faster = hotter).
Pressure is explained as the momentum transfer of those moving atoms on the walls of
the container (faster atoms = higher temperature = more momentum/hits = higher
pressure).

Ideal Gas Law

Ideal Gas Law:
Macroscopic properties of matter are governed by the Ideal Gas Law of chemistry.
An ideal gas is a gas that conforms, in physical behavior, to a particular, idealized
relation between pressure, volume, and temperature. The ideal gas law states that for a
specified quantity of gas, the product of the volume, V, and pressure, P, is
proportional to the absolute temperature T; i.e., in equation form, PV = kT, in which k
is a constant. Such a relation for a substance is called its equation of state and is
sufficient to describe its gross behavior.
Although no gas is perfectly described by the above law, the behavior of real gases is
described quite closely by the ideal gas law at sufficiently high temperatures and low
pressures (such as air pressure at sea level), when relatively large distances between
molecules and their high speeds overcome any interaction. A gas does not obey the
equation when conditions are such that the gas, or any of the component gases in a
mixture, is near its triple point.
The ideal gas law can be derived from the kinetic theory of gases and relies on the
assumptions that (1) the gas consists of a large number of molecules, which are in
random motion and obey Newton's deterministic laws of motion; (2) the volume of the
molecules is negligibly small compared to the volume occupied by the gas; and (3) no
forces act on the molecules except during elastic collisions of negligible duration.

Thermodynamics

Thermodynamics:
The study of the relationship between heat, work, temperature, and energy,
encompassing the general behavior of physical system is called thermodynamics.
The first law of thermodynamics is often called the law of the conservation of energy
(actually mass-energy) because it says, in effect, that when a system undergoes a
process, the sum of all the energy transferred across the system boundary--either as
heat or as work--is equal to the net change in the energy of the system. For example, if
you perform physical work on a system (e.g. stir some water), some of the energy goes
into motion, the rest goes into raising the temperature of the system.

The second law of thermodynamics states that, in a closed system, the entropy
increases. Cars rust, dead trees decay, buildings collapse; all these things are examples
of entropy in action, the spontaneous movement from order to disorder.

Classical or Newtonian physics is incomplete because it does not include irreversible
processes associated with the increase of entropy. The entropy of the whole Universe
always increased with time. We are simply a local spot of low entropy and our destiny
is linked to the unstoppable increase of disorder in our world => stars will burn out,
civilizations will die from lack of power.
The approach to equilibrium is therefore an irreversible process. The tendency toward
equilibrium is so fundamental to physics that the second law is probably the most
universal regulator of natural activity known to science.
The concept of temperature enters into thermodynamics as a precise mathematical
quantity that relates heat to entropy. The interplay of these three quantities is further
constrained by the third law of thermodynamics, which deals with the absolute zero of
temperature and its theoretical unattainability.
Absolute zero (approximately -273 C) would correspond to a condition in which a
system had achieved its lowest energy state. The third law states that, as this minimum
temperature is approached, the further extraction of energy becomes more and more
difficult.