# The Physics of …

We know that Amazon wants your opinions to be heard. However, sometimes authors have paid for fake reviews or even created them under false identities. Whatever your thoughts on this type of thing, be sure that having great reviews can help your book sell.

Lots of people are trying to make money by exploiting writers” – says Michele Gorman , “(…) But a writer’s best chance of success is to write good books that lots of people honestly enjoy. Taking shortcuts by paying for fake reviews cheats readers. It cheats our own integrity. And it damages the reputation of the vast majority of book bloggers whose only payment is a free book in return for an honest review.”

Personally, I consider reviews to be critical in the sales process; comments and suggestions are always a great way of helping me continue to enhance my knowledge, my communication skills to talk about math and physics and in words that everyone can understand.

I am hopeful that my book has helped you enjoy learning. I am extremely grateful to have been given this opportunity and I have no idea what’s going on in … reviews!

# Big Bang Theory

The Big Bang theory explains the beginning of the universe’s expansion, what happened during and after that moment.  According to the standard theory, this theory states that the universe began from an initial point (singularity: zone of infinite density), which has expanded over billions of years ( around 13.7 billion years ago) to form the universe as we now know it. In 1922 Alexander Friedmann of Russia is credited with developing a dynamic equation for the expanding universe.  We are taught that the universe began as a singularity – an infinitely small and infinitely dense point. Once the singularity was created, it began to expand through a process called inflation.

After that, it expanded and cooled, going from very small and very hot, to the size and temperature of our current universe. Astronomers observed the relationship between the number density of distant radio sources and quasars( quasars are intense sources of X-rays as well as visible light) and the energy received from them per unit area per unit time have discovered new evidence about the rate at which the universe is expanding. The research shows a slow enough expansion to explain the ages of the oldest globular star clusters, as long as the universe has a low density.

Observational evidence

Stockton observed faint galaxies near in the sky to bright quasars at moderate redshifts. The redshift of an object is the amount by which the spectral lines in the source are shifted to the red.

Quasars are associated with galaxies that have the same redshift as the quasar and have just the brightness expected if the quasars are at their cosmological distances. The redshift caused by the expansion is often confused with the redshift generated by the Doppler effect.

The Doppler redshift and the cosmological redshift are governed by two distinct formulas. The first comes from special relativity; the second comes from general relativity.  If the redshift is interpreted as a Doppler shift, the recessional velocity of the object can be calculated. In an expanding Universe, distant objects are redshifted, with $z = H_0D/c$ for small distances. This law was discovered by Hubble and $H_0$ is known as the Hubble constant.

At large distances, the conversion between cosmological redshift and distance is much more complicated, depending on the geometry of spacetime and the expansion history of the Universe.

Big Bang Theory – Evidence for the Theory
The universe had a beginning. Galaxies appear to be moving away from us at speeds proportional to their distance. This is called “Hubble’s Law,” named after Edwin Hubble (1889-1953) who discovered this phenomenon in 1929. This observation supports the expansion of the universe.

In 1965, while tuning a small, yet very powerful and highly sensitive horn antenna for conducting radio astronomy experiments, Arno Penzias and Robert Wilson noted a constant low level noise disrupting their reception. They discovered a 2.725 degree Kelvin (-454.765 degree Fahrenheit, -270.425 degree Celsius) Cosmic Microwave Background radiation (CMB).

The Universe’s light-element abundance is another important criterion by which the Big Bang hypothesis is verified. Light elements (namely deuterium, helium, and lithium) were produced in the first few minutes of the Big Bang, while elements heavier than helium are thought to have their origins in the interiors of stars which formed much later in the history of the Universe. It is observed that upwards of 25% the Universe’s total matter consists of helium. The Big Bang Nucleosynthesis theory predicts that 25% the mass of the Universe consists of Helium. It also predicts about 0.01% deuterium, and even smaller quantities of lithium. The important point is that the prediction depends critically on the density of baryons (ie neutrons and protons) at the time of nucleosynthesis. Measurements of the baryon density in the Universe using the cosmic microwave background spectrum and primordial nucleosynthesis constrain the baryon density to a value less than 0,05.

There are a number of free parameters in the Big Bang model must be fixed by observations of our universe: the geometry of the universe (open, flat or closed); the present expansion rate (the Hubble constant); the overall course of expansion, which is determined by the fractional density of the different types of matter in the universe.

# Under Pressure

“Pressure pushing down on me
pressing down on you no man ask for
under pressure”

###### (lyrics from “Under Pressure”)

Pressure is the ratio of force applied per area covered:

$P= \frac{F}{A}$

The unit of pressure is the pascal:

The pascal is also a unit of stress and the topics of pressure and stress are connected.

Pressure in a uniform fluid.

• The gauge pressure in a uniform fluid at a particular depth is directly proportional to …
• the density of the fluid ρ,
• the acceleration due to gravity g, and
• the depth h.

The absolute pressure in a uniform fluid at a particular depth is given by:

$P=P_0+\rho gh$

Atmospheric pressure

Atmospheric pressure is defined as the force per unit area exerted against a surface by the weight of the air above that surface.

Boyle’s Law(after Robert Boyle, Irish scientist, around 1600)

Boyle’s law states that, at a constant temperature, the volume of a given mass of gas varies inversely with pressure. For two states of pressure (P1, P2) and two corresponding volumes (V1, V2), this is stated mathematically:

$P_1V_1=P_2V_2$

Charles’ Law (after Jacques Charles, French scientist, around 1790)

By warming the balloon up, we increase the speed of the moving gas molecules inside it. This in turn increases the rate at which the gas molecules bombard the skin of the balloon. Because the balloon’s skin is elastic, it expands upon this increased pushing from inside, and the volume taken up by the same mass of gas increases with temperature. In consequence, the density [=mass/volume] decreases with rising temperature. Cooling the balloon down again will make the balloon shrink.

Thus Charles’s law states that at a constant pressure, the volume of a given mass of gas is directly proportional to its (absolute) temperature. For two states with temperatures (T1, T2) and two corresponding volumes (V1, V2):

The Ideal Gas Law or Equation of State

The example used to illustrate Charles’s law probably does not follow Charles’s law exactly. It is very likely that, during the heating process, when the rate of collisions by the gas molecules increased, the pressure increased as well as the volume. Thus, in practical situations all three variables involved in Boyle’s and Charles’s law are linked and both principles are in action at the same time:

 Pressure: P Temperature: T Density: r = m/V

These variables describe the state of the gas at any one time and are combined in the single relationship known as the ideal gas law or the equation of state:

Dalton’s Law of Partial Pressure:

The pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented as:

PressureTotal = Pressure1 + Pressure2 … Pressuren

Pascal’s Principle:

Pascal’s principle states that a pressure applied to an enclosed fluid is transmitted everywhere in the fluid. Hence, if a pressure is applied to one side of an enclosed fluid, all the other walls containing the fluid feel the same pressure. The pressure is transmitted without being diminished.

In physics, if a pressure is applied to a compressible gas, Pascal’s principle still applies, but the volume of the gas will change. For Pascal’s principle to be useful to hydraulics, the fluid should be an incompressible liquid, which will transmit the applied pressure without changing its volume.