Today’s Shared Post_Link: 10 April 2017

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The Mystery of Entropy (1)
What is entropy and what does entropy have to do with order and disorder? We know what order is. The concepts of order and disorder have been part of our consciousness since long before the notion of entropy was ever invented.” …

What Order Is
Order is having everything in its proper place, behaving in its proper manner. Disorder is the opposite… Order is a well tuned machine with all its parts moving in perfect coordination with all other parts. A machine with parts not behaving as they should is a machine that is out of order… Order does not necessarily involve movement… In other words, order can be dynamic or static.” …

Pop Quiz
So what is entropy? Probably the most common answer you hear is that entropy is a kind of measure of disorder. This is misleading. Equating entropy with disorder creates unnecessary confusion in evaluating the entropy of different systems. Consider the following comparisons. Which has more entropy?
– stack of cards in perfect order or a stack of cards in random order?
– a Swiss watch with intricate internal workings or a sundial?
– ten jars of water stacked neatly in a pyramid or the equivalent mass of water in the form of 10 blocks of ice flying randomly through space?
– a living, breathing human being or a dried up corpse turning to dust?
– the universe at the moment of the Big Bang or the universe in its present state?
If you think of entropy as disorder, then the answers to these questions may trouble you.” …

Entropy According to Classical Thermodynamics (2)
Let’s take a look at where the idea of entropy actually came from. The concept of entropy originated around the mid 19th century, from the study of heat, temperature, work and energy, known as thermodynamics. This was the era of the steam locomotive. The study of how heat could be most efficiently converted to mechanical work was of prime interest…

…heat always flowed from hot to cold. The challenge was to find the most efficient way to harness heat flowing out of a hot reservoir toward a cold reservoir and use it to do mechanical work…

This became the operational definition of a newly conceived property of systems, a property which came to be know as entropy. (The term was coined in 1865 by Rudolf Clausius who thought of it as representing a kind of “internal work of transformation”.) Simply stated, entropy is the relationship between the temperature of a body and its heat content (more precisely, its kinetic heat energy).

Entropy, S, is the heat content, Q, divided by the body’s temperature, T.
S = Q/T
Stated another way, the heat, Q, stored in an object at temperature, T, is its entropy, S, multiplied by its temperature, T.
Q = T x S

That is it. The definition of entropy, as originally conceived in classical thermodynamics, had nothing to do with order or disorder…

The entropy of system is the average heat capacity of the system averaged over its absolute temperature.” …

The Significance of Entropy in Classical Thermodynamics
The significance of entropy in the study of heat engines and chemical reactions is that, for a given temperature, a system can hold only a certain amount of heat energy – no more and no less – depending on the entropy of the system.

In chemistry entropy meant that calculating the change in chemical energy, the energy represented by the making and breaking of chemical bonds, was not enough to predict how much useful energy would be released during a reaction. The amount of energy “freed” by a reaction was the energy generated by the chemical reaction minus any additional energy trapped by changes in the system’s entropy. The additional energy trapped was just the change in entropy, delta S, times the temperature of the system, T. In 1876, J. Willard Gibbs named this useful energy released as “free energy” and provided the formula to calculate it. The free energy, delta G, was the change in chemical energy, delta H, minus the trapped, thermal energy, T times delta S.

delta G = delta H – (T x delta S)” …

Entropy According to Statistical Thermodynamics
… Temperature was determined to be the average kinetic energy of all the different ways the molecules could move, tumble or vibrate. This more detailed, molecular, perspective of thermodynamics and the mathematics associated with it became known as statistical thermodynamics.

On average, molecules with more kinetic energy lost kinetic energy as they collided and molecules with less kinetic gained kinetic energy as they collided, until, on average, the kinetic energy was optimally distributed among all the molecules and their various modes of movement.

The greater the number of kinetic energy pockets a system had, the greater its entropy. So, on the molecular level, entropy was just a measure of the total number of molecular kinetic energy pockets contained in the system.” …

Entropy As Disorder
It was Boltzmann who advocated the idea that entropy was related to disorder. In Boltzmann’s mind, the more ways a system could move internally, the more disorderly the system was. A system in “perfect order” was one in which all the molecules were locked in perfect array without any freedom of movement whatsoever. A dynamic system in perfect equilibrium represented, according to statistical thermodynamics, a system in “perfect disorder”. The idea of entropy as a measure of disorder was embraced and perpetuated by his colleagues in the field of statistical thermodynamics.” …

Problems With Entropy As Disorder
But is disorder really the best word to use to define entropy? I don’t think so. There are several problems with using disorder to define entropy. The first problem has to do with systems having multiple levels of organization. A system might be more or less “orderly” on one level and not at all on another. Take the example of the ice cubes flying around in space. On the level of the ice cubes, the system is disorderly, but on the molecular level, the ice molecules are locked in place, neatly in order.

The second problem with disorder as a definition for entropy, in my mind, even on the molecular level, is that disorder implies things are not where they should be. This is not the case. Movement on the molecular level is still governed by Newtonian mechanics.

The molecules are, in fact, exactly where they should be. Where else could they be? They are not free to make any random turn or jump between collisions. The rules are clear – continue straight between collisions and then strictly obey the laws of conservation of energy and conservation of momentum during the collisions.

Entropy should not and does not depend on our perception of order in the system. The amount of heat a system holds for a given temperature does not change depending on our perception of order. Entropy, like pressure and temperature is an independent thermodynamic property of the system that does not depend on our observation.” …

Entropy As Diversity
A better word that captures the essence of entropy on the molecular level is diversity. Entropy represents the diversity of internal movement of a system. The greater the diversity of movement on the molecular level, the greater the entropy of the system. Order, on the other hand, may be simple or complex. A living system is complex. A living system has a high degree of order AND an high degree of entropy. A raccoon has more entropy than a rock. A living, breathing human being, more than a dried up corpse.” …

Answers to Pop Quiz
With this clearer understanding of entropy, let’s take a look at those troubling entropy questions posed earlier…

As for the watch and the sundial, it depends. If they are both made of similar metals and they are at the same temperature and pressure, then on a molecular level they would have about the same entropy. The molecules in the watch would have about the same diversity of movement in the solid metal parts as the molecules in the metal of the sundial. Ounce for ounce, the heat content would be about the same for both.

On the higher system level, you could say the watch has more entropy than the sundial because it has a greater diversity of internal movement. The watch has more internal kinetic energy than the sundial. What significance you could give this “higher level” entropy is not clear to me.” …

The Big Picture
So that brings us to the universe as a whole. This is very problematic. At the time of the Big Bang, there were no molecules. Is it really appropriate to talk about entropy, temperature and heat at this level? Does undifferentiated plasma have kinetic energy? What about the universe today? What is the temperature of the universe? What is the temperature of any system that is not homogeneous and not at thermal equilibrium? These are not trivial questions. The temperature and entropy of a system is only well defined for systems that are homogeneous and in thermal equilibrium. The easier way to answer the entropy of the universe question is to accept the 2nd law of thermodynamics and extrapolate backwards. The 2nd law says entropy is always increasing in the universe, so the entropy of the universe at the time of the Big Bang must have been much less that the entropy of the universe now.

This does not mean there was more structure or order back then. It does mean there was less diversity and less space to move around. The evolution of the universe has been characterized by an on-going transformation from a simple, restricted, highly condensed, homogeneous state to an increasingly complex, widely dispersed, dynamic, multipotent, granular diversity. In other words, the universe is not winding down, like a giant soulless machine slowly running out of steam. On the contrary, she is just waking up.” …

Read the complete article with update and comments… Click author’s link: 

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Entropy Is Not Disorder by Steve Donaldson in Science 2.0 Blog

Photo Credit: Entropyhyper physics: Thermal entropyEntropy, Order, Disorder and Energyandelion chocolate

… she is just waking up …

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