In this age of technology, we depend on gadgets and machines for almost all of our basic needs throughout the day. Machines wake us up, prepare our breakfast, transport us to work, light up our homes, provide us means to get entertained, and what not. At the heart of all our appliances, there is a mechanism that uses up energy to accomplish a specific task. In the common, day-to-day vocabulary, energy is something which we always want to conserve to reduce our monthly bills. But what is energy? The law of conservation of energy claims that the energy is conserved, and can neither be created nor destroyed, so why do we care so much about its conservation when the conservation law does not allow its destruction? How does the energy flow and transform into different forms and what bearing does that have on the past and the fate of our Universe? Where does all this immense amount of energy present in our Universe come from? Would it ever be depleted? If yes, what drives the process of depletion of energy, and how would that end all existing life forms, and perhaps everything around us? In this essay, I delve into the thermodynamic and mathematical descriptions of energy and entropy in the light of the Second Law of thermodynamics, and why the Second Law is a fundamental law of physics that is essential to describe the past and the fate of the Universe.
A. Energy
Energy is defined as the capacity of the system to do work. What is work? Wikipedia defines work as the energy transferred to or from an object via the application of force along a displacement. As you can see, the definitions of energy and work are the statements which reference each other, and it is not possible to explain one in terms of the other without getting caught up in a regress. This takes me back to my 9th Grade, and reminds me of a chapter in our science textbook that discussed the basic concepts of motion, energy and work. Those textbook definitions still fall short of explaining work and energy independently of each other. This incompleteness served as a partial inspiration for me to write this essay. Let's dive straight into some hard core physics now.
A.1. What exactly is energy?
Every physical system is described by a set of equations; if the equations of a system remain fixed and unchanged, then a system variable which is time invariant (that does not change with time) is defined as the energy of the system. The reader is advised not to confuse fixed equations with a strictly time stationary or steady system. Equations may be fixed, but their solutions are not, and it is the solutions which determine the fate of the system. As the time passes, the state of the system described by its position and velocity changes, with only one quantity being constant -- that is energy. A convenient example would be that of a swinging pendulum. As the pendulum swings between the extremities through its mean position, the energy of the pendulum constantly changes from potential to kinetic and back to potential. However if you sum the partitions of kinetic and potential energies at any point of time, you will end of with a same number. Mathematically, this property that does not change with time in the case of systems whose equations are fixed and unchanging, is called energy.
A.2. Conservation of energy
Since we have established that energy, by definition, is a property which is time invariant, or conserved, then why do we worry about its conservation at all? Why not just keep our appliances plugged in and our lights on all the time? The answer to this question is the quality and the nature of the energy changes when its is converted and dissipated as heat. A burning chunk of coal burns until the chemical energy in its bonds is released in the form of heat. It is this chemical energy that drives our steam engines, thermal power plants and keeps our traditional Kashmiri Kangris* searingly hot. Once the chemical energy of the bonds is released as heat, even though the sum of the left over chemical energy and the dissipated heat will add up to a constant, the part of the energy dissipated as heat is rendered unavailable for useful work. The energy dispersed to surrounding air molecules is lost forever to randomness. This is where entropy comes into the picture. The energy available for useful work is called free energy and the energy lost to randomness is heat. While the total energy is conserved, it is this free energy which is not conserved. When we turn off a gadget, we are actually talking about conserving and saving this free energy, and not simply energy.
There are some violations to the law of energy conservation at cosmic scales when we consider the expansion of the universe and the redshift of electromagnetic radiation, but for the present discussion, it is reasonable to neglect those effects.
B. Entropy
Consider a video of a bunch of balls striking against each other on a pool table. If you play the video backwards, the laws of physics seem to be obeyed just as if the video were played forwards. The energy transfer between the balls as they strike each other is exactly equivalent in both the cases. Energy flows backwards in time in exactly the same way as it does forwards. If we take a step further and consider chemical or nuclear reactions, the law of physics would still be symmetrical in time, meaning no matter if we play a reaction backwards or forwards, the laws would not be violated. If there is no difference in how the laws of physics behave from a temporal perspective, backward reactions should be possible, yet we don't see it happen! Why doesn't the heat from the flames end up building the chemical bonds in the chunk of coal again? The reason why such reactions don't occur is the Second Law of Thermodynamics. It is the only law of physics which does not work the same way backwards in time as it would forwards.
The Second Law of Thermodynamics dictates in what direction a process proceeds spontaneously. Spontaneous processes tend to maximize dissipation, and tend to carry the system towards the state of equilibrium. For example, let's say we have a box with two compartments joined together by a small hole and that we start with 6 gas molecules in the left compartment. How would the system evolve over time? Would just one molecule pass over to the right compartment, or two, or three or all of them? Would the molecules just stick together in just one compartment? What would happen to the probability of finding a molecule in either one of the two compartments? The Second Law of Thermodynamics dictates that the system of these 6 gas molecules will end up evenly distributing the gas molecules throughout the box, in both of the compartments. If only 1 molecule is carried over to the right compartment, the number of ways that can be done is \( C(6,1)= 6\), similarly if 2 or 3 molecules end up diffusing to the right compartment, the number of ways that can be arranged are \( C(6,2)=15\) and \( C(6,3)=20\) (Please note that 4, 5 molecules diffusing to the right compartment is an equivalent situation of 2 and 1 molecule(s) diffusing as the combinations come about to be the same.) As we can see, the arrangement in which the gas diffuses evenly ( \( C(6,3)=20\) ) between the compartments has the maximum number of ways of happening. This is what will happen to our system, probabilistically speaking. The ways of arranging the molecules between the compartments are called microstates**, and the configuration with the maximum number of these microstates is the one with maximum entropy. This is the reason why we don't see the molecules in the box collecting back in one compartment, or the air in our kitchen getting displaced towards just one corner. The Second Law of Thermodynamics prevents that from happening, for purely probabilistic reasons.
B.1. The Second Law of Thermodynamics and the origin of the universe
Someone may ask, why do we bother to add the Second Law to the list of the fundamental laws of nature when we can predict the future state of the gas in a box by using Newtonian laws of motion by computing their momenta, given their initial position? The answer to this question is that the Second Law informs us about the initial conditions present at the beginning of the universe, and it is the only law of physics which has the ability to differentiate between the past and the future, i.e. it is unsymmetrical in time unlike the rest of the fundamental laws. Since other fundamental laws are symmetrical in time, it is only the Second Law which explains why we don't live in the universe that has its entropy always at the maximum possible value. Without the Second Law, the universe would arise with a set of initial conditions that would lead to the entropy increase or decrease with forward flow of time equally unlikely. In other words, the initial conditions that would lead to such scenarios of increasing or decreasing entropy would be highly unlikely. And yet when we look at our universe, we see that entropy is constantly increasing with time. This is only possible if the Second Law is a fundamental law of our universe right from its origin until its end. The information about the low entropy state of the universe at the beginning is something that is only derived from the Second Law. This is what makes the Second Law a fundamental law of physics.
C. The end of life and the universe
Since we have established that we live in the universe in which the entropy is constantly increasing with time. The lighter nuclei in the stars would be exhausted, and converted into elements that are no longer useful for fusion. When this happens, no new stars would form. Eventually, when all the elements that sustain nuclear fusion will be depleted, all the energy will be dispersed. This means that the universe is headed towards a state of thermal equilibrium in which the thermodynamic free energy is zero, and would therefore be unable to sustain processes that increase entropy. This is a state when our universe would attain its maximum entropy, the possibility of the existence of any life in such a scenario is zero, as life essentially thrives on the mechanisms that dissipate free energy. As no free energy is there to dissipate, there is no chance of life to exist after such point.
 |
| Source: Aeon - Timelapse of the future |
Our memories, art, literature, science, music, differences, friends, foes, wars, triumphs, achievements, failures, emotions, aspirations, communities, families, love, hate, envy, hope and all that has ever existed -- will all extinguish and get lost under a thick and dreadful curtain of indifferent and eternal darkness! What made the universe to appear in the first place, or the reason and the secret behind it all is not with those you follow, it is not with the clergy or high priests or Imams, it is not with the people who tell you to kill those who don't follow your religion, it is not with those who bomb and terrorize others for whatever reasons, it is not with those who tell you what to do or what not to do, or that following a certain ritual will book you a spot in some fantasy called heaven, or that failure to follow a certain ritual will end you up in hell. The secret of the universe is way greater than all of these naiveties, and greater than what we can ever imagine. Our place in this vast void is at best insignificant.
Meanwhile, let's be good to each other, irrespective of our differences, what we look like, our skin color, our gender, and what God we believe in!
Cite as
Bader, Shujaut H., “The Second Law of Thermodynamics: origin and the end of everything." Backscatter, May 12, 2021. https://backscatterblog.blogspot.com/2021/05/the-second-law-of-thermodynamics-origin.html
Footnotes
* Kangri is an earthen pot woven around with wicker filled with hot embers used by Kashmiris beneath their traditional clothing pheran to keep the chill at bay. Source: Kangri Wikipedia
** For a detailed discussion on microstates please refer to my earlier essay, "Entropy and disorder: from genes to messy rooms!"
Comments
Post a Comment