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Avogadro and His Number

Avogadro’s Hypothesis

In 1811, Amedeo Avogadro (1776–1856) (born Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto) looked at Gay-Lussac’s results and concluded that when they are at the same temperature and pressure, equal volumes of gas (like two balloons of the same size) contain the same number of “particles.” These particles can be individual atoms, molecules, or even a mixture thereof.

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The Cosmic Machine: Table of Contents

[Contents]

I

The First Law: Energy

1 Nothing for Free
The Conservation of Work

2 Swinging, Falling, and Rolling
The Initial Foundations of Energy

3 Untangling the Mess
Energy, Momentum, Force and Matter

4 The Missing Link
Heat Was the Final Piece to the Energy Puzzle

II

Nature’s Compensation: Entropy

5 Thoughts of Heat Engines
The Thermodynamic Origins of Entropy

6 Dissipation
The Relationship Between Heat and Work

7 The Preferred Direction
Entropy as Nature’s Sign Post

8 The Other Side of Entropy
Entropy’s Connection to Matter and Atoms

III

The Pieces: Atoms

9 Speculations of Atoms
Thoughts of Existence Pave the Way for Atoms

10 Two New Philosophies
Rational Versus Spiritual View of Nature

11 Realizing Atoms
The Physical Foundations of the Atom

12 Final Doubts to Rest
The Atom as Physical Reality

IV

Uncertainty: Quantum Mechanics

13 Discrete
Energy’s Devious Secret

14 Light Quanta
Particles and Waves: The Beginning

15 The Quantum Atom
Revisiting the Atom

16 Quantum Mechanics
Nature’s Lottery

Epilogue
From Here to There

Pharmacological Characterization of 1-(5-Chloro-6-(Trifluoromethoxy)-1H-Benzoimidazol-2-yl)-1H-Pyrazole-4-Carboxylic Acid (JNJ-42041935), A Potent and Selective HIF Prolyl Hydroxylase (PHD) Inhibitor

T.D. Barrett, H.L. Palomino, T.I. Brondstetter, K.C. Kanelakis, X. Wu, P.V. Haug, W. Yan, A. Young, H. Hua, J.C. Hart, D.T. Tran, H. Venkatesan, M.D. Rosen, H.M. Peltier, K. Sepassi, M.C. Rizzolio, S.D. Bembenek, T. Mirzadegan, M.H. Rabinowitz, N.P. Shankley, Mol. Pharmacol. 79, 910 (2011).

 

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Light and An Ideal Gas

In 1905, Einstein’s comparison between dim (or dilute) light, and an ideal (dilute) gas led him to conclude that under certain conditions, light will behave as a particle.

Einstein on Planck’s Derivation

“[Planck’s] derivation was of unparalleled boldness, but found brilliant confirmation. … However, it remained unsatisfactory that the [classical mechanical] analysis, which led to [Planck’s Radiation Law], is incompatible with quantum theory, and it is not surprising that Planck himself and all theoreticians who work on this topic incessantly tried to modify the theory such as to base it on noncontradictory foundations.” –Einstein

The Ramifications of Quantum Mechanics

The Problem with Schrödinger’s Wave Equation

The biggest question still plaguing Schrödinger’s wave equation was the role of the wavefunction. Sure, mathematically it’s clear: it’s the solution to Schrödinger’s wave equation and the “all-powerful function” as a result. However, physically it was still a big mystery to everyone, including Schrödinger himself.

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Einstein’s Miracle Year 1905

In 1905, at the age of 26, Einstein published four major papers and finished his PhD thesis. Each of these papers was groundbreaking and would change physics forever.

Early Atomic Theories

Thoughts of Existence Pave the Way for Atoms

The ancient Greek philosophers played a significant role in shaping the initial thoughts about atoms and early atomic theories. Several of the ancient philosophers pondered and developed a theory of matter, with one even imagining the existence of a fundamental building block that made up not only all living and nonliving things, but the supernatural as well. Their thoughts were speculative and philosophical, rather than scientific in nature. And while they attempted to touch on the nature of matter and its composition, their real goal was to address something of profound concern to the ancient Greeks: the nature of permanency and change. Unfortunately, these “theories” of matter were rather short-lived. Although there was some revival during the Middle Ages and the Renaissance, they never gained any real momentum until the seventeenth century.
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Bose’s Derivation of Planck’s Radiation Law

With his work in 1916-7, Einstein was able to arrive at a “much more” quantum derivation of Planck’s Radiation Law. However, in the end he fell short, having to rely on assumptions. In 1924, Satyendra Nath Bose provided the first “fully” quantum derivation of Planck’s radiation law, which revealed the deeper nature of light that had eluded everyone else, including Einstein.  With this work, he created the new area of physics known as quantum statistics.

Einstein’s Paper on Brownian Motion

In 1905, a young Albert Einstein wrote a paper (while working as a patent clerk) on a well-known physical phenomenon of the time, Brownian motion, which had first been noted in 1827. Einstein’s theory correctly described Brownian motion, and at the heart of his theory was the existence of atoms that were in constant motion.

 

Brownian_motion_V3b

Light and Einstein

Einstein Revisits His Theory of Light

By 1911, Einstein had already hypothesized that light consists of particles he called light quanta (later called photons). Moreover, he had shown that light has an inherent quality, whereby it exhibits both wave and particle properties. Although, he had seen further than anyone into the mysterious nature of light, it continued to perplex him:

“I do not ask anymore whether these [light] quanta really exist. Nor do I attempt any longer to construct them, since I now know my brain is incapable of advancing in that direction.”

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Entropy and The Second Law

The Finer Points of Heat

 By 1852, Thomson had come to believe that heat could be both transformed into work, as described by Joule’s theory, and free flowing to produce no work at all, as described by Fourier’s theory. In the latter, heat was simply dissipated, but not lost in accordance with the first law. Moreover, he distinguished between high quality and low quality energy and insisted that the universal tendency for energy is to dissipate as heat, making it unavailable for work. But Thomson wasn’t the only one thinking about the finer points of heat … so was Clausius.
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Einstein’s Nobel Prize

In 1921, Einstein won the Nobel Prize. The citation reads:
“To Albert Einstein for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect.”

To be sure, Einstein is being acknowledge for the “the law of the photoelectric effect”, in other words for his photoelectric equation, but not for the photon concept. This attitude would persist until 1923, when new experimental results would convert pretty much everyone to the existence of photons.

Entropy, Microstates and Boltzmann

Ludwig Boltzmann‘s Early Career

Ludwig Boltzmann (1844–1906) was born in Vienna and attended the University of Vienna, where he received his doctorate in 1867. Boltzmann was a restless spirit, changing (by choice) from one academic position to another, a total of seven times in his almost forty-year career.

From the early 1870s on, Boltzmann was a scientific superstar and very much in demand. To get Boltzmann to accept a professorship of theoretical physics at the University of Vienna in 1894, the Austrian minister of culture had to offer him the highest salary then paid to any Austrian university professor. Boltzmann had already been a professor at the university of Vienna twice before, once from 1867–1869 as an assistant professor, and a second time from 1873–1876 as a professor of mathematics. Nonetheless, in 1900 he left for a third time.

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The Speed of Atoms and Kinetic Theory

James Clerk Maxwell

James Clerk Maxwell (1831–1879) was born in Edinburgh, Scotland, in 1831. His family moved to a small country estate in Middlebie, Galloway (southwestern Scotland) that his father, John Clerk inherited (the addition of the name “Maxwell” was required to satisfy legalities of this inheritance). When he was eight, James’ mother died, of abdominal cancer; she was forty-eight. John Clerk Maxwell was an attentive and perhaps overly protective father. Unfortunately, he made the mistake of entrusting James early education to a tutor who employed beatings as a teaching tactic. Fortunately, a visit from his maternal aunt, Jane Cay, discontinued this abusive treatment, as she was able to convince Maxwell’s father to allow him to continue his education at Edinburgh Academy.

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The Thermodynamic Origins of Entropy: Carnot and The Heat Engine

Carnot, Caloric Theory and The Heat Engine

In 1823 when Sadi Carnot (1796–1832) began this task, less than thirty years had passed since Rumford’s cannon-boring experiments led him to declare “heat is motion”. And although this should have been the end of caloric theory, it and its principle of heat (caloric) conservation were mostly undaunted. Further, a more complete understanding of energy would have to wait for some thirty years for the first law to be established.

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Bohr and The Atom

Niels Bohr’s Early Career

In March of 1912 Niels Bohr (1885–1962) arrived in Manchester to begin working with Rutherford. Previously, he had worked with Thomson in Cambridge. Unfortunately, their relationship had been strained from the start, and never really flourished as Bohr had hoped. Writing to his brother Harald, Bohr said:

“… Thomson has so far not been as easy to deal with as I thought the first day. …”

Perhaps, Bohr’s initial encounter with Thomson was to blame, where upon entering Thomson’s office, Bohr proclaimed:

“This is wrong.”

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The Universal Tendency of Energy

William Thomson’s Struggle with Heat and Work

In 1847, when William Thomson (later Lord Kelvin) (1824–1907) learned of Joule’s experiments (on the mechanical equivalent of heat) demonstrating that work could be converted to heat, he immediately recognized the impact of this discovery. Moreover, it was clear, although not explicitly demonstrated by Joule’s experiments (but nonetheless claimed by Joule), that this equivalence meant that one would expect the conversion of heat into work to be possible as well. This caused problems for Thomson, since at that time, he was still a proponent of caloric theory, which stood in direct opposition to Joule’s conclusion.

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Write, Edit, Fact Check, and Repeat

Edit, Edit, Edit …

For those of you that have been following along, I am at the editing stage in my book-writing journey (to then be followed by adding figures, more editing, a last round of fact-checking, formatting, index creation, and then (cross your fingers for me), finally publishing this (hopefully) masterpiece. Oh yes, and the book cover. I found a great designer (Derek Murphy) and am having him put the finishing touches on. Check out the latest and greatest and give your input: Book Cover Survey

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Galileo, The Ingenious Experimenter

A major concept of the book was to connect the science with the actual story around it. This aspect endowed the book with a lot of fascinating science history and biographical information about the scientists. I particularly enjoyed the stories of how Galileo cleverly overcame the many obstacles he encountered when performing his experiments. Enjoy this excerpt from the book.

Galileo Galilei

Galileo Galilei was born the oldest of seven children in Pisa on February 15, 1564 to Vincenzo Galilei and Giulia Ammannati. His father was both a music practitioner and music theorist. Although a number of his compositions were published Vincenzo made only a meager living as a performer and teacher.

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Caloric Theory and Heat

Pierre-Simon Laplace Viewed Heat to be Comprised of Particles

Pierre-Simon Laplace (1749–1827) imagined heat to be a fluid composed of particles, deemed by Antoine Lavoisier (1743–1794) as caloric. Whereas the particles comprising ordinary matter were considered to be attracted to each other, caloric particles were considered to repel each other (by today’s standards it may seem strange to describe heat as a type of particle but light, another imponderable fluid, was also being promoted as a particle, especially by Newton himself).

The fact that the particles of ordinary matter were attracted to each other seemed to be consistent with experimental results: cooling a gas results in the particles moving towards each other to form the more compact liquid structure, and subsequent cooling moves the particles even closer together resulting in the solid structure when something freezes.

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Max Planck’s Rough Road to Quantum Theory

Max Planck’s Early Life

Max Planck (1858–1947) was born in Kiel, (in modern day Germany), the sixth child to the distinguished jurist and professor of law at the University of Kiel, Johann Julius Wilhelm Planck and his second wife, Emma Patzig. His family culture would bestow in Planck’s life and work a sense of excellence in scholarship, incorruptibility, idealism, reliability, and generosity.

In 1867, when Planck was nine, his father received an appointment at the University of Munich. The family moved and Planck enrolled in the city’s Maximilian Gymnasium where his interest in physics and mathematics was piqued. However, Planck excelled in his other studies as well, in particular music. Thus at the time of graduation, now 16, Planck had the difficult decision of choosing a future in either music or physics; he chose physics.
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Carnot the Outsider

During his formal education Sadi Carnot (1796-1832) was literally surrounded by renowned physicist, chemists and mathematicians on the faculty. However, Carnot was never a member of this distinguished group, and did his most important work (as a founder of modern day thermodynamics) as an outsider.

Zero Point Energy

The zero point energy of a system is a direct consequence of the Heisenberg uncertainty principle.

The Intensity of Light

In terms of quantum theory, increasing the intensity of light means increasing the number of photons.

Compton Scattering

In 1923, Arthur Compton’s (1892-1962) light scattering experiments provided further support for Einstein’s hypothesis for the particle nature of light.

Solid Helium

Although possible, helium does not easily solidify due to quantum effects related to its small atomic size.

Why is The Sky Blue?

Shorter wavelength blue light is scattered more by air molecules than red light. It’s this “Rayleigh scattering” that results in the blue color of the sky.

The Superheated Liquid

When a liquid has been heated to a temperature above its boiling but still doesn’t boil, it’s superheated.

The Supercooled Liquid

If a liquid is cool rapidly enough it can miss the freezing point and end up as a supercooled liquid.

An Amorphous Solid Versus A Glass

While all glasses are amorphous solids, not all amorphous solids are glasses; glasses exhibit an actual glass transition. Even though we say solid, a glass is actually a very viscous liquid that moves very slowly over time.

Glass is Really a Liquid

The glass in a window (for example) is really a very viscous liquid that moves very slowly over time.

When a Light Bulb Burns Out

A light bulb is more likely to burn out when first turned on since this is when the electrical resistance is the lowest. As the current flows it heats up the wire and the atoms begin to “jiggle”, which increases the electrical resistance.

The Weight of Heat

The chemist Lavoisier actually tried to weigh heat; he found it was weightless.

Speed of Sound and Material Phase

The speed of sound depends on the phase of the material (solid, liquid, or gas). In general, sound travels fastest in solids, then liquids, then gases.

Feynman on Why We Need Math

“If you want to learn about nature, to appreciate nature, it is necessary to understand the language [of mathematics] that she speaks in. She offers her information only in one form; we are not so unhumble as to demand that she change before we pay any attention.” -Feynman on Why We Need Math

The Resistance to Einstein’s Light Quanta

Einstein’s light quanta hypothesis met with tremendous resistance, taking almost twenty years after its introduction in 1905 to be fully accepted. Despite such opposition, Einstein continued to use the concept in his work with significant success.

Laser

A laser is possible because photons are Bosons and not Fermions.

Matter in transition

Democritus saw material objects (matter) as existing in a temporary state, being created or destroyed as atoms respectively come together or fall apart under the influence of natural forces; all that remains then are the atoms comprising those material objects.

Atomos and Atoms

Democritus considers everything in the universe – including the human mind and soul, and even the gods – to be comprised of atomos, which is Greek for indivisible and from which we get “atom”.

Dalton and Atomic Weights

With a firm belief in atoms, impressive physical insight and armed with a few simple rules, Dalton was able to construct a table of relative weights, which he first presented in 1803 at a talk to the Literary and Philosophical Society of Manchester. In 1805, this effort first appeared in print, with a systematic explanation of the method appearing in 1808 when Dalton published the first volume of his book A New System of Chemical Philosophy. Here, with hydrogen as his reference, he gave the following relative weights: hydrogen (H) 1; nitrogen (N) 5; carbon (C) 5.4; oxygen (O) 7; phosphorus (P) 9; sulfur (S) 13 and so on, including several elements and compounds.

Newton on Light Diffraction

Newton felt there were some properties a wave theory of light simply could not explain, such as diffraction. For example, diffraction is the property of waves that allow them to bend around objects and spread through openings. In the case of sound waves, it’s why a sound in one room can often be heard in another room farther away by someone not directly in the path of the oncoming sound; the sound wave travels from the one room, spreading out through the doorway into the other room where it’s then heard. Light doesn’t appear to behave this way, after all, you can’t see around corners – can you? The diffraction of light is usually unnoticeable because light waves have such short wavelengths – much smaller compared to the wavelengths of sound waves. Nonetheless, light will diffract if the opening is small enough.

Wave-Particle Duality

In 1905, Einstein established wave-particle duality for light. In 1923, de Broglie extended it to all quantum particles. In an interview in 1963 de Broglie reflected on his epiphany:

“As in my conversations with my brother we always arrived at the conclusion that in the case of X-rays one had both waves and [particles], thus suddenly – … it was certain in the course of summer 1923 – I got the idea that one had to extend this duality to material particles, especially to electrons.”

The speed of light

The speed of light was measured as early as 1862 by Leon Foucault giving good agreement with the modern value of 299,792.458 Km/s.

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